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By 'concrete impacts' I mean hard data for example: CO2e emitted, harm to the ecosystem, resources depleted, cost to the economy, etc.
I have a piece of clothing that is broken that I want to get rid of, and I want to know if it's worth the trouble.
ETA: re-using them, for example as cleaning clothes might be the next best thing, but what if I already have enough of those or the clothing piece in question can't really be used for that purpose?
That will very much depend on the material from which it is made. Assuming that the clothing cannot be repaired, the next best thing to do is to re-use it - for example, cut the cloth into squares and use them for cleaning, instead of buying new cleaning cloths.
This is highly variable depending on the material. For example, if the textile is made from oil-based materials (i.e. plastics), disposing it improperly might accelerate the microplastics problem in oceans. You could:
Cotton also contains carbon, has an energy content and can be recycled, so the options and their impacts are the same. This time, however, cotton doesn't accelerate the microplastics problem. On the other hand, cotton has a large water footprint, so if you believe water scarcity is a major problem, you could recycle it, hoping less new cotton will be produced and less water will be used to do that.
I don't know what the EROEI of cotton is; if it's low you should consider ideally other options than burning because it doesn't make sense to use materials having poor EROEI as an energy source. Low EROEI materals should be ideally recycled; high EROEI materials can usefully be burned to energy to offset other fossil fuel uses.
