There is some good information at medirabbit.com
Dosage: 10 - 100 mg/kg (up to 400 mg/kg)
Method and Frequency; By Mouth 1 to 3 times daily
Aspirin is a blood thinner and must therefore be avoided in case there are internal bleedings or when
surgery is planned
Dosage: 0.1 - 0.2 mg/kg (up to 1.5 mg/kg if needed)
Method and Frequency; By Mouth or subcutaneously 1 to 2 times daily
Very palatable for rabbits
Concurrent use with another NSAID, corticosteroid, or nephrotoxic medication must be avoided. If unavoidable, the rabbit should be monitored closely.
Long-term use appears to cause little adverse effects in rabbits
Should not be used in rabbits suffering from liver or kidney failure
I know for sure (from several rabbit specialist vets and BSAVA Formulary) that meloxicam is very safe for use in rabbits, even long term (one of mine has been on it for 2+years and it's a life saver for him, you can see immediate deterioration when a dose is missed, so I know it works and works well), at 0.3-0.6 mg/kg daily (0.5 being the minimal recommended) and doses as high as 1.5 mg/kg are well tolerated for several days. PLEASE NOTE this is not the case for carnivores and any overdose will cause blindness.
I run a rabbit rescue for ill animals so am medicating many of them at any given time. I have never used aspirin and, having seen several rabbit specialist vets with various rabbits, was never prescribed any aspirin for any of my rabbits; is always been meloxicam only. I shall ask my vets why this has been the case and try to follow up later.