TL;DR: At the tailpipe, a diesel vehicle and a CNG vehicle have roughly equal greenhouse gas emissions. But taking into account leaks in the natural gas production systems, the diesel vehicle is probably the better choice from a climate change perspective.
Google Scholar returns a surprising number of results when you search "vehicle carbon emissions CNG vs diesel" (since 2017). Many of the results are locked behind paywalls, but one of the most interesting is not.
Alternative Fuel Life-Cycle Environmental and Economic Transportation
First is the Alternative Fuel Life-Cycle Environmental and Economic Transportation (AFLEET) Tool from the U.S. Argonne National Lab. From the description:
The tool uses data from Argonne's Greenhouse gases, Regulated Emissions, and Energy use in Transportation (GREET) fuel-cycle model to generate necessary well-to-wheels petroleum use and GHG emission co-efficients for key fuel production pathways and vehicle types. In addition, Environmental Protection Agency's MOtor Vehicle Emission Simulator (MOVES) and certification data are used to estimate tailpipe air pollutant emissions. Various sources are used to provide default cost data, including the Clean Cities Alternative Fuel Price Report and American Recovery and Reinvestment Act awards.
I downloaded the tool and compared light-duty gasoline, diesel, battery electric, and CNG vehicles.
UPDATE: Argonne National Lab just released a web-based version of AFLEET where you can do the same comparison yourself.
Here's the result in terms of externality costs for the four types of vehicles:
To remove the ambiguity inherent in how externalities are counted, here's the raw emissions data ("LD" is for "light duty," the vehicle type I selected):
To answer your question directly at this point... per year, when driving 16,500 miles (26,500 km):
- A diesel vehicle will produce 4445 kg CO2 equivalent
- A similar vehicle fueled by CNG will produce 4536 kg CO2 equivalent
Leaks in natural gas production systems
Although it looks like a wash at this point, as @THelper pointed out, one other factor to consider is methane leakage from natural gas production systems, as methane is 25 times more potent as a greenhouse gas than CO2 in the short-term.
An article in Science on this topic made headlines earlier this year. The article, "Assessment of methane emissions from the U.S. oil and gas supply chain", is behind a paywall, but Phys.org has a good summary. Here's the most significant finding (emphasis added):
[R]esearchers found most of the emissions came from leaks, equipment malfunctions and other "abnormal" operating conditions. The climate impact of these leaks in 2015 was roughly the same as the climate impact of carbon dioxide emissions from all all U.S. coal-fired power plants operating in 2015, they found.