I think it's a difference for being on offense vs defense. In a high streak prize fight, Trauma Center will probably serve you better, because Valentine is almost certainly not going to be you main damage dealer. What you really need is for your main damage dealer not to die if you make a mistake, which is where Trauma Center is more useful. Plus you have SG, who will take them from 1 hp to a point where they can block again. I've used a SG for that exact purpose for a very long time now, and it's worked really well for me.
Being able to revive people is great, but it's tricky, and ICU is not going to do a huge amount to keep Valentine alive in a high streak prize fight, where it's possible for one combo to kill you sometimes.
ICU is better for defense or if you're fighting in the daily/weekly events, because the enemies are already weaker than you generally, and it's only the debuffs that can really pull you down.