I don't know anything about Accredo, but I know the other two. I used to use Caremark for my Pulmozyme and am now using Triessent. I have never been a fan of mail order pharmacies. I would much rather go pick it up at my local pharmacy, but since these insurance companies require it for certain meds, there's nothing I can do about it.
It seems like there was some issue with Caremark when I first started with them, but after that I never really had any problems (used them for several years).
My husband's employer recently changed ins. carriers and now we have BCBS which uses Triessent (and some other that I can't recall). Depending of which med you need, they have like 3 different mail order pharmacies (very confusing). I am only on Pulmozyme so I can't speak for the TOBI. Initially, it was a pain in the butt. I was given wrong information (which in turn got me denied for assistance with help with the co-pay which is $150). I specifically asked these people about the co-pay and the supply amount because we were tight on money and was told by all three people that it was a 90-day supply with a co-pay of $150. When it showed up it was only a 30 day supply. Needless to say, I was not a happy camper! After several phone calls and everything was straightened out, I haven't had any issues, but I have only been using them since March.
Hopefully, that helps you. I know each person has a different experience, but, at this point (at least for me), I would go with Caremark. But, again, that's just my opinion.