Random thought. Note that the comparisons are subjective. It's my perception and opinion. Also, some people may appreciate the story of FFXIII better after reading. OR you may end up hating it even more for lack of originality. I personally feel XIII has a good story, but it has fail storyTELLING. This is what probably make FFX>>>>>>FFXIII to a majority of people.
SPOILERS FROM X AND XIII
Will edit later if I find more similarities.
SPOILERS FROM X AND XIII
-Character/s who mysteriously get transported into another world (Tidus-->Spira, Vanille/Fang-->Cocoon)
-These two worlds, apparently or literally have a gap of hundreds of years
-These characters who appear on a new world has a mission in this world (Tidus='save it', Vanille/Fang='destroy it', until their focus changes to 'save it')
-They are present in this new world due to divine/magical intervention (the Fayth and Auron, Fal'cie)
-These character/s adapt and interact with the world. They find some things weird/unfamiliar (for FFXIII, this is seen in episode 0)
-A journey to save the world (save Spira from Sin, save Cocoon from destruction)
-Special powers given to the character/s (Summoner Yuna, L'cie powers/eidolons)
-After fulfilling the destiny, they will die/sleep for eternity (Yuna dies if she had summoned the final aeon/Tidus disappears in the end, crystallisation occurs after completing focus)
-fugitives in most part of the game ('killing' Seymour, Pulse Fal'cie)
-Finding out that the true enemy is someone you wouldn't expect (Yunalesca, Barthandelus)
-Defy divine powers (Yevon, Barthandelus/Orphan)
-An ending where people want to create a new world (Spira, Pulse)
-and lastly....a sequel (FFX-2, FFXIII-2)
-These two worlds, apparently or literally have a gap of hundreds of years
-These characters who appear on a new world has a mission in this world (Tidus='save it', Vanille/Fang='destroy it', until their focus changes to 'save it')
-They are present in this new world due to divine/magical intervention (the Fayth and Auron, Fal'cie)
-These character/s adapt and interact with the world. They find some things weird/unfamiliar (for FFXIII, this is seen in episode 0)
-A journey to save the world (save Spira from Sin, save Cocoon from destruction)
-Special powers given to the character/s (Summoner Yuna, L'cie powers/eidolons)
-After fulfilling the destiny, they will die/sleep for eternity (Yuna dies if she had summoned the final aeon/Tidus disappears in the end, crystallisation occurs after completing focus)
-fugitives in most part of the game ('killing' Seymour, Pulse Fal'cie)
-Finding out that the true enemy is someone you wouldn't expect (Yunalesca, Barthandelus)
-Defy divine powers (Yevon, Barthandelus/Orphan)
-An ending where people want to create a new world (Spira, Pulse)
-and lastly....a sequel (FFX-2, FFXIII-2)

Will edit later if I find more similarities.