Visuals:
I think the game world of ToT is much, much prettier than AP's. Better lighting, richer colours, a somewhat more fluid camera, nice visual effects that aren't in AP (i.e ambient dragonflies and butterflies). Buildings look bright and cheerful in ToT; in AP, I feel they're quite dull looking and washed out by comparison. Ripping and comparing them side by side, I noticed that many of AP's textures are considerably poorer quality than ToT's. I'm mystified as to why this all is. I wish AP could be that pretty.
Characters:
Both games have largely the same cast of characters. ToT has two characters who have appeared as marriage candidates in several games throughout the series, namely Grey and Elli, but sadly you can't marry either of them in this game. Disappointing, but given that, it's just as well that they are absent in AP. ToT unfortunately has no special marriage candidates, either - the Harvest King, Wizard, and Witch aren't present, and you can't marry the Harvest Goddess.
I like AP's male protagonist a lot more than ToT's, because I think Kevin looks too much like a little boy. I thought Angela's model in ToT was so much nicer than either her or Molly's AP model though - the body shape was smoother and better proportioned, and every outfit doesn't have a weird built in tanktop/vest piece.
The roles, personalities and outward appearances of most characters are mostly the same in both games - in ToT Perry is an assistant at the clinic; in AP he is the keeper of the local church, which I like better, since it is eerily empty in ToT (though if he's still Jin's cousin in AP, it is never commented on). I like that Luna is taller and somewhat less bratty in AP; in ToT she looked and acted like a ten year old girl. If I didn't know already I would never have guessed she was a marriage candidate, and honestly, it makes me a bit uncomfortable. Owen is an extremely tall and muscular stud in ToT, but in AP they totally ruined his proportions, making him much shorter and shrinking down his muscles... me no likey. Grrr.
In ToT I fell in love with Jin's character, which goes into a lot more depth with his backstory. As you get closer to him,
Spoiler:
On area where ToT totally fails IMO is with the player's children. They all have boring personalities and generic appearances. My kid with Chase bore an uncanny resemblance to Gill, besides the eye and hair colour... Hmmmm.
Story:
The basics of the main plot of ToT and AP are the same: help the five harvest sprites in order to save the Harvest Goddess. However, I feel AP's story is much better, more in depth and better paced. It is also a lot simpler to complete - ringing the five bells in AP is much easier than gathering the ingredients for the five rainbows in ToT, many of which are difficult and time consuming to obtain, which makes it super tedious.
Spoiler:
For the most part, I'd say AP is the winner here. In AP the clock is twice as slow and time does not pass indoors (which it does in ToT), and that is a huge bonus for me, because I don't feel rushed all the time. In ToT, you can't separate stacked items, like herbs, and a lot of items such as ores don't stack at all - it seems like such a minor thing, but this drove me absolutely insane with frustration. Among other things, in AP there are more crops to grow, the circus animal quest chain that will enable to teleport you around the island if you complete it, building hearts with everyone is easier, you can ride on all of your livestock, and you can actually get your spouse and kids to help with farm work. The only thing I liked better in ToT was being able to pick and choose from different plots to place your farm buildings, like in MM - in AP your house, coop, barn, and plots are always in the exact same place, and this can't ever be changed. ToT also allows a lot more customization for the inside of your house, too, like in MM - there is a larger variety of furniture to pick from, and you can move almost anything you want, wherever you want. In contrast, AP doesn't let you move most of your furniture, such as your bed and kitchen table, and there are very few places that it will let you place movable furniture. Kind of a bummer, but c'est la vie.
There, that's my two cents. Please don't tear me shreds!