I'm one of those people, so I'll comment.
FFRK feels more like FF not because of the story (obviously - it has none), but overall; the Characters are FF, most of them are lifted directly from there previous games sprite-sheets, they don't feel out of place even though they've reduce to 16-bit sprites, they have not been redrawn to fit a non-FF theme. The music is lifted directly from previous FFs. The abilities and magic are (mostly) from previous games. The strategies fit the FF theme (use boss weakness, or some other hokey~interesting tactic etc.) the SBs are themed to each character (with a few odd exceptions). The UI is FF (although painfully slow).
FF:BE; It's a 'Brave'-game, with FF characters popped in (so randomly in-fact, that when you pull them from their crystals they have no idea why they are even there - and most of the time I shared that same sentiment - does the story explain this? I'm only at the 2nd continent). The battle system is 'brave', the characters sprites and animations are 'brave' (expect the monsters oddly - this is also odd since Yoshitka Amano drew them, and they're still more brave than FF), the UI is 'brave', the story is 'brave', the music is 'brave' (Noriyasu Agematsu). None of this a bad thing - but you're fooling yourself if you think this is more FF than brave.
FF:Mobius - (after about 3hrs - so this may be way off) feels like a modern FF (unfortunately), with it's angsty 'whatever' main character, annoying girly-voiced moogle (why cant they bring back cool-moogle from FFIII/VI?), an interesting combat system that feels very XIII inspired, and a card system that I hope I have not figured out yet. The music is FF. The UI is FF. The graphics have that annoying EARLY physically-based-material feel that FFXIV has, that tries really hard to look real, but doesn't (I don't know how to explain it) it ends up looking 'flatish' and kinda washed out - maybe they did this on purpose to make it feel like FFXIV? but overall you can tell it's a FF game.
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