If 饭店 is a more formal restaurant than 饭馆, where would you situate 餐馆? More like an eatery, more low-key than 饭馆 or more formal than 饭店? Are there other differences in meaning between the three words?
There is no "Official" Classification as one might expect as, like any socio-cutural Centri activity, it is subject to the fashions of the day and Times.
However, there is some informal consensus, though no one opinion is carved in stone.
Lets take the Western classification first, as there is some general consensus on what is what, and why, and feel free to dispute what I have to say below.
Restaurant == a very general term to mean a business establishment where meals or refreshments may be purchased; not much help here as it is too general a term to pigeon hole it.
Fine dining restaurants == called white-tablecloth restaurants, serving expensive cuisines.
Bistro == a restaurant, serving moderately priced simple meals in a modest setting.
Brasserie == a type of French restaurant with a relaxed setting.
Osteria == a place serving wine and simple food.
Cafeteria == a restaurant in which customers serve themselves from a counter and pay before eating.
Now, where do 饭馆, 餐馆, 饭店 fit into all these, or there is no correlative comparison at all?
My personal view is, rightly or mistakenly:-
All three could be called "restaurants", but if one wants to do an academic classification, then:-
饭馆 & 饭店 could both be informal establishments, and so more like 3,4,5, above.
餐馆, like "餐厅", could fall into 2 above.
I don't think traditionally there is such a thing as "Cafeteria" in Chinese victual history where coffee is the main attraction, though there were Tea Houses, (茶馆, 茶楼, 茶亭, depending on where in China they are found), which of course falls outside of our present discussion.
Finally, 饭店 has sometimes taken to mean a hotel, though a more accurate term is 酒店, which is a strange term in itself and deserves more research.
And 路邊攤, (as @r13 said), are "hawkers" or "street vendors", which to the pathetic poor, may very well be their "restaurants"