It's a very broad (perhaps too) broad question because "other image classifiers" can mean literally anything. The good thing about HMMs is that they are statistical (as opposed to heuristics and hand-made rule-based classifiers), they are quite robuts, and they can classify vectors/images of variable dimension/length (unlike many other classifiers where all the input vectors must have the same dimension). Disadvantages: I'm not a real expert in this, but I guess it might be that they need quite a lot of training data, and also that it often happens that all possible HMM trajectories have actually "near zero" probability and the classification is thus problematic because the classifier is forced to choose the optimum among many almost same improbable options.
If you need a general HMM toolbox for Matlab, try Kevin Murphy's here http://www.cs.ubc.ca/~murphyk/Software/HMM/hmm.html
But if you're looking for a ready-made visual image classifier (btw, you actually mention "images", but it's not clear whether you mean visual images, or rather more abstractly images in the sense of "classification patterns... but I guess the first option is right), then unfortunately I don't know, it's not my area. However, it doesn't have to be too hard to build an image classifier on tom of the Kevin Murphy's toolbox.