My mind tends to categorize them in three part era installments mostly due to the three game per console thing they started with. Obviously there's liberties taken for the stuff post X due to random releases, spinoffs and MMO's, but for the most part I see it like this:

FFI - FFIII ---> NES era (The old skool era)
FFIV - FFVI ---> SNES era (The retro era)
FFVII - FFIX ---> PS1 era (The "my-first-FF" era)
FFX - FFXII (including X-2) ---> PS2 era (Testin' the waters era)
FFXIII - FFXV (plus MMO's/Type-0/Stranger of Paradise) ---> PS3/PS4 era ---> (50/50 era/franchise era)
FFXVI - PS5 era ---> (Modern era..... for now)

Silly bracketed captions aside, that's pretty much how I see them. Also, there was so much going on around that PS3/PS4 era with things like series within series (Fabula) and long development hells (FFXV née Versus XIII) and other spinoffs of varying quality and intent that it kind of all seemed like one era as opposed to PS3 and 4 being two separate ones. You know, in case anyone was wondering