I interviewed at New Britain last year and I am currently a junior student at Bridgeport Hospital. The program director and all of the students at New Britain seemed very nice and overall I came out with a good impression of the program.
My major concern about the program however was the amount of clinical experience. The OR itself is pretty small, if I am remembering correctly 8 rooms but don't quote me on that. They also have to send students away to get their regional experience because they are not able to get enough in house (though this is not uncommon in many programs I did not really like the idea). In general the program has a good reputation but is regarded as more of the "country club" program than the others in the state, more laid back, get out early (when I was interviewing at about 1PM the students were leaving for the day), etc... Which is not necessarily a bad thing but just something to keep in mind.
As far as competing with residents that shouldn't be a problem, to my knowledge New Britain does not have a residency program (at least in anesthesia).
The interview itself was pretty basic, interviewed with the program director and a few CRNAs none of the MDs. They did ask some clinical questions but nothing too hard.
I hope this helps.