ThinkFast007:
When you say "chief," you aren't talking about a resident, right? I just want to be clear...
As for which letter will carry more weight, I would get letters from people who KNOW you the best and can write YOU the best letters. Those types of personal letters from attendings may carry the most "weight," because they'll be top shelf "real" letters from people who will likely put that extra effort into writing how great you are, what a pleasure you have been to get to know, what a great addition you would make to any department including their own, and how dissapointed they are that they couldn't convince you to go into their field (if it's not anesthesia). I would, however, add in your anesthesia chairmen's letter. Personally, I'm not really into the whole "weight" thing for LORs, but it is funny how chairmen know each other. Anesthesia is a small world. Trust me...you will find out just how small when you're on the interview trail.
As has already been mentioned by previous posters, Keep in mind that all your letters don't have to be anesthesia/SICU/critical care related. I ended up using a total of three letters from three different fields, and only my anesthesia chairmen's letter was directly related to the field of anesthesia.
MedicinePowder:
To answer your other question, I didn't do any ICU/critical care rotations or away rotations. I did all my rotations at my home school, and I only did one anesthesiology elective. I had fun, enjoyed myself, and got into an excellent anesthesia residency.