Browser crashed on me after I wrote a long post, so I'll just give bullet points. Note that a lot of these don't end up applying because folks tweak or ignore them.
--Pay attention to initiative and particularly its effects on casters.
--In Basic, clerics don't get a spell at 1st level (though in B/X, they get that weird jump where they go from 2/2 at 5th level to 2/2/2/1/1 at 7th).
--Pay attention to the way magic spells are learned and how many you can have. In B/X, magic-users only know as many spells as they can cast per day (so if you can cast 3 first level spells per day, you only know 3 first level spells).
--What kind of armor can effective fighter/magic-users (including race-as-class elves) wear?
--What attribute generation method does the edition use, and can you allocate your stats as desired or pull points from certain attributes to put into others?
--Where do bonus modifiers start? In AD&D, for instance, you tend to have much significantly attributes before you start getting a plus than you do in Basic (then again, AD&D endorses a more generous method of stat generation).
--What kind of morale rules, if any, does the game have.
--in OD&D, all hit dice are d6s (see pic for how that works, though pic is actually from Swords & Wizardry White Box), which is nice, because it means that a +1 bonus to hit points will affect everybody by the same percentage, rather than having a much bigger impact on magic-users than fighters.
--What do you get experience points for and how much do you get for them?
--In addition to level caps (are these affected by your prime requisite?), are there attribute maximums and minimums per race and gender?
--Are there attribute requirements for classes so stringent that it's almost impossible to get into some of them?