I've been blessed with a few great offers so far (USC, UCSD, CMU-Pitt) in Biomedical Informatics for this coming fall. I'm still awaiting one more university, but (unfortunately -- Pitt is a great school) my choice (if Stanford doesn't pan out) will either be USC or UCSD. That being said, a sore point for me is UCSD's stipend which is around $33,000 for PhD students. I also was told when I went to campus that on-campus housing/subsidized housing is scarce, and $33,000 is not a great living stipend in an area as expensive as La Jolla. UCSD other than that is my top choice, mostly given my research area (genetics of autism). USC is my alma mater, and they just got back to me today offering me $36,000 a year, but with an award topping it off to $41,000 the first two years. I also believe there's fairly guaranteed funding all four years or more through TA/RA. If it wasn't a matter of finances, I feel despite the generous offer that UCSD may be more aligned with my career direction interest (USC is a very computationally-focused program, vs UCSD which is closer to 50/50 bio/CS depending on your interests).
On that note, I have two potential PIs at UCSD, one who has expressed his strong interest in me joining his lab. His research area seems to align really closely to mine (genetics of childhood neuropsychiatric disorders).
Given those factors, would it be disrespectful or even possible to ask for a higher stipend to compare to another offer? I come from the industry world of CS where this is not only common but actively encouraged. That being said, this is really my first foray into academia so I'm not sure that's a possibility here.