One thing to remember is that virtually all cutting near a patient -- clothing or whatever -- is going to be done with shears, not a knife. I've been an EMT for years, and I can't remember ever having to cut a seatbelt. Always been able to reach the buckle... 'rescue' knives are appealing but are far from essential.
That said, I usually carry an Assist or a hawkbill (Tasman or Crossbill, and sometimes lately a Spyderhawk), and have a multitool (Vic. Spirit or one of an assortment of SAKs) and a small general-purpose knife handy. They get used for opening packaging more than anything else.
A knife is more useful in the firefighting side of emergency services than in EMS, though.
This post on the Spyderco company forum is by a Chicago firefighter. He's gotten a little bit of use out of the Tasman he keeps on his bunker gear.
I'd lean towards a fixed blade for a knife attached to bunks, though, and leave the folders for pocket carry in your uniform pants. Maybe a Caspian Salt. (Just got accepted by my local volunteer department, so I'm going to be having to make this decision soon myself...)