It seems to me the essential definition for a game to be an RPG, J or W, should be the extent to which you define your character's role and personality through A) the depth of control over the development of a character's gameplay mechanics and or B) control on the story progression as that character. That is to say, to play the role of a character, you should be able to play out how that character would respond to a situation and not be forced to follow a linear path. Both of these factors come in different doses, and while there can be no universal RPG line, the dose determines to what extent a game is a role-playing game. For instance, choosing what kind of weapon you wield is indicative of what you determine as your character's preference; in this way both Mass Effect and Zelda have RPG elements, but Mass Effect has a higher dosage of RP (strictly considering how much preference you can put into the which and the how in a weapon).
This is not to say games have to have both of these factors to be an RPG, consider Diablo 2 and Chrono Trigger: in Chrono Trigger you as a character have a strong influence over how the story progresses and ends but your character's stat progression is automatic and linear(if I recall correctly), whereas in Diablo 2 you have a open ended character development but otherwise, in terms of choice, you have a few quests you do not have to do and maybe some different arrangements in the order, but the plot and its ending remain the same. Both are RPGs from different hemispheres with distinguished but undeniablely role-playing characteristics.
By this definition, some games that are traditionally considered RPGs are not so much (Final Fantasy VII, linear in character and story development other than some nice Cloud or snarky Cloud dialogue choices and materia arrangement - FFVII is pretty light on RP). WRPGs, particularly from Bioware and Bethesda, flourish on this definition, as they typically focus on delivering these qualities. JRPGs, regardless of the quality of the story, do seem to tend to be more linear (with linearness in a way being the antithesis of an RPG).
My favorite heavy RP RPGs: Mass Effect, KOTOR, Demon's Souls
My favorite light RP RPGs: Super Mario and the Legend of the Seven Stars, Dark Age of Camelot, Nox, The World Ends with You
On a side note, a lot of recent Western RPGs which are being hammered for not having as strong a core story still establish lush settings with lots of small appreciable stories that make to me, a richer story atmosphere than occurs in most JRPGs.