there is usually a difference in terms of quality. a lot of hosting sites downgrade the quality of your photos and do not inform you (redownload them from the host, compare to original, and you'll see)
some store platforms (like bigcartel) are very restrictive in this point. i've found workarounds for the background/logo and stuff like this (simple things), but doing that for all the product pics would be a bit more than i want to worry with. bigcartel images are not the same resolution as the original files, it sucks.
i'd host them yourself, especially if you are leaning towards doing an art site. if you can in your platform, at least.
also, 'graph paper press' does some very pretty art-site templates. with lookbooks and such. responsive themes. check them out.
ONE THING I SHOULD MENTION ABOUT DREAMHOST! they very explicitly do not allow server space to be used simply for storage (like a personal dropbox). if you have a folder full of music which isn't utilized in your website, just on the server, they can/will remove it. i'm not sure if this is the same elsewhere, but dreamhost i know is on the lookout for this sort of thing