The question seems to be asking only about the environmental impact of the cartridges, so I probably shouldn't talk about how a laser printers use 100 times more power while they are printing, but allow me just to say that for the whole life cycle the most significant stage for both types is paper usage, followed by the manufacturing of the product and electricity consumption.
According to energycentral.com the production of a new laser cartridge consumes more than three quarts of oil emitting close to 5kg of greenhouse gases per cartridge, while inkjet cartridges consume about three ounces of oil with a corresponding reduction in GHG during manufacture. This factoid is found all over the web without naming the source, and it bothers me further because it doesn't take into consideration the differences in size and capacity.
Both types of cartridges also require a lot of steel to produce (the plastic is just a coating) but it's important to note that 97% of the materials used in both types of printer cartridges can be recycled, which means you can effectively reduce the waste to only 3% if you return them to the manufacturer or drop them off at Best Buy or Staples to get your coupon towards your next purchase.
You can reduce that further if you refill your own, but many printer manufacturers try to foil your attempts to use refilled or re-manufactured cartridges. In 2017, the Supreme Court told Lexmark it can’t make it impossible for printer cartridge buyers to refill them, but it didn't say they couldn't make it awkward or difficult.
If you plan to buy a new printer, look for a brand that doesn’t goof around like that. When comparing, keep in mind that each time a cartridge is refilled, the impacts of refilling get added to the total footprint, but the increase of the cartridge’s life reduces the overall impact.
Many sources quote each other that GHG emissions by weight for the toner are about 16 to one, which works out to 3.2 kg GHG per 200 grams of toner, but I have not been able to find the original source of these numbers either.
Toner is basically plastic polymer dust, which is considered a hazardous waste in Europe, but only if it is being disposed of or being sent to recycling, not if it's being refilled. Toner in some ways is considered less dangerous to the environment than aqueous inks because many of the chemicals needed in inkjet ink are not required in a laser printer.
Inkjet cartridges are considered a "designated" item by the U.S. EPA. which mandates that any government agency, office or contractor that spends more than $10,000 a year on inkjet cartridges must purchase a model with the highest levels of recycled content. Naturally, this would not apply to you if you are just buying one for your own personal use.
A good study of Life Cycle Assessment of toner cartridges can be found here https://pdfs.semanticscholar.org/6023/3272d8efc645494fb1a4a15f24f80a8a386a.pdf?_ga=2.260727236.830309716.1565737019-1061069556.1565737019 but it compares toner according to different recycling alternatives, not to inkjets.
A good LSA for inkjet printers which includes the ink can be found here https://www.researchgate.net/publication/276385268_Life_cycle_assessment_of_an_inkjet_printer
The best Life Cycle Assessment (LCA) I have found that breaks down all the factors by comparison can be found at https://scholarworks.rit.edu/cgi/viewcontent.cgi?referer=https://www.google.com/&httpsredir=1&article=1093&context=books which should be examined if you want all the hairy details. Although standards for carbon footprinting exist (including WBSCD’s GHG Protocol, ISO14064 and the draft PAS
2050) there is no absolute guidance for deriving boundaries for a study of this type.
Typical Material Safety Data Sheets for inkjet cartridges can be found here http://www.hp.com/hpinfo/community/environment/productinfo/pdf/ij_c6635a_eng_v1.pdf The table entries marked "confidential" would be the ones I would be most concerned about. This may be the reason why a fair comparison of between the two technologies has not yet been presented to the public.
The part of the discussion that never seems to come up is something I've noticed from personal experience. Most people throw out the inkjets when they run out of ink because a new printer with ink costs a lot less. This seldom happens with laser printers. From the point of view of the cartridge, the problem is compounded when the printer runs out of only one color ink, leaving the other three to be wasted. This is a huge black mark against the sustainability of inkjets in practice, but the end result is that you can get all kinds of inkjets for free if you intercept them as post consumer waste, effectively reducing the manufacture impact to zero while simultaneously reducing the load on landfills.
In short, the differences between the impact of the cartridges themselves is minuscule compared to many other factors that would be significant when choosing between the two technologies. From the perspective of sustainability, I would opt for the laser, especially if my source of power is guaranteed to be clean, but when I can't generate enough power, I am often forced to use the inkjet.
The printed paper, from both inkjet and laser printing, after it's been printed and goes to recycling, gets stripped of inks and resin which is removed from the pulp in a form of sludge that doesn't always get used for anything else. It could be used in making composite deck planking and other construction materials, but it doesn't have much commercial value and is often thrown into the landfill. Nevertheless, it sometimes ends up as fertilizer, or is burned to create energy.
After repulping the paper, the pulp gets treated with deinking enzymes (usually a mixture of cellulase and hemicellulase) and mixed with a non-ionic surfactant (basically soap) during flotation which helps the enzymes to soak in and prevents the ink from re-attaching itself to the fibers.
The cellulase itself is a natural enzyme that breaks down cellulose. It's produced by bacteria, fungi and protozoans in the natural environment as well as inside our digestive tract to break down fruits and vegetables. The PH sometimes needs to be adjusted, so if the paper contains a lot of sizing (like clay or ash particles) then a mild acid is used to lower the alkalinity. If it needs to be raised (due to acidic paper) then sodium silicate or sodium hydroxide is used. If the paper needs to be very white, then hydrogen peroxide is use to bleach the inks, which is considered very safe in the environment.
Often, different types of cellulase may be matched with different types of surfactant to get best results or simply to avoid having to alter the PH level. The water itself is easily recycled and gets fed right back into the system. Some operations use DAF (dissolved air flotation) with a small amount lost through evaporation.
Energy also has to be added to the system in the form of heat (45 to 55 C), but you don't want it to get too hot (65C) or the toner particles will fuse again to the pulp fibers. The sludge from deinking is sometimes burned to provide this heat.
In most all office paper recycling operations, the printed ink jet paper and printer toner sheets both go through the same process because those two waste streams are not sorted. They get sorted out as "Office Waste" (OW) but they don't get sorted out from each other. It is possible to sort them and treat them differently, resulting in a simpler process for the paper without toner, but this is only done in very specialized waste streams where the volume is high and the quality of the feedstock is certain.
So, unless paper recycling methods change, the environmental impact of both types of recycled paper is very nearly identical. It's important to note that this process is primarily used only when the brightness of the paper is an important outcome. Very often in unsorted waste streams the final product is cardboard and neither the ink nor the toner needs to be removed. It just gets blended into the final product with (hopefully) no difference at all on the impact to the environment.
What is completely unknown is what actually happens to the thousands of chemicals in paper during and after the recycling process. Until the secret ingredients of printer inks and toners are revealed, there is no way to know. Those ingredients are considered "confidential" in the industry. Until then, no comparison can be made.
In the recycling industry, upcycling is never considered. Paper is believed to be useful only to create same or lower quality products. Since collection and retention of water is the primary concern in the arid desert where I live, all waste paper products get converted to compost. My personal sustainability depends on a huge population of worms who would get very hungry and thirsty if they didn't have ample food and a moist habitat. They can sometimes consume half their weight every day. Paper is one of their favorite foods, and it holds moisture well. When planting trees I dig enormous holes and fill the bottom with layers of paper, branches, rotted manure, native soil, and finished compost. Initially, this does little more than provide a bank for water, but it also assures the future survival of the tree by providing a nourishing roots zone and a place for worms to survive if the surface gets too hot, too dry, or too cold. I view this as "upcycling" because the end result (fresh, fermented, dried, and canned fruit) is much more valuable to me than any kind of paper. I'm not sure why, but my nut trees seem to get a special boost from paper, especially when it's shredded and mixed into the top 18 inches of mulch.