Admittedly Stan doesn't work for all problems, but where I've seen a lot of issues in "bad" performance by Stan is when people try to fit models that are unidentified or weakly identified. Unlike some other algorithms which will give back the wrong answer quickly with the user none the wiser, Stan's HMC will try to do what the model says - sample over the whole unidentified space, and it takes a while to sample R^n. What I've seen in Stan's mailing list is that in practice a lot of people have been fitting poorly identified models without realizing it.