Here's some examples of streamlined actions:
Your character actually runs rather than "lightly jogs" like in Animal Parade, which means you move around faster; plus, you can buy a horse or construct a vehicle (albeit later in the game) to move around even faster. Also, with the power to jump, you're no longer bound to going around fences; just jump over them.
In Animal Parade (and I presume ToT, though I never played it), when you upgraded your farming tools, you would hold the A button to "charge" them. You would have to hold for a certain number of seconds in order for the charge to reach its maximum size. In ANB, the charge happens in less than a second and it expands from one square to its maximum number of squares immediately. So farming takes overall less time, especially when you upgrade your tools. The same goes for chopping down trees: it only takes one swing and you're done, compared to the multiple swings of Animal Parade. At some point in the main story, you receive access to "tiered farmland," which is a massive space where you can plant lots of crops and then have the local spring water everything for you immediately. It's a beautiful sight.
Mining is completely overhauled to be more convenient. You simply have a large room with three mining 'spots' that you hit with your hammer, along with any randomized goodies laying on the ground. As you upgrade your hammer, you'll get access to more of the spots, and each time you hit the spot, you'll receive an item. Compare this to Animal Parade, in which you you were never certain if anything valuable would come out of a rock (and sometimes you received something annoying like poison gas) and even when you found ore, the "refining" process might give you crap in return. In ANB, there's none of this guesswork: you don't have to refine ore, you simply get the gem or material that comes out of the mining spot. And if you don't like what you receive, you can simply reload your save at that point and try again (thanks to the fast loading).
Lastly, town customization means that you can eliminate unnecessary running. In Animal Parade, you had to run all the way across town if you wanted to buy things or talk to people. Here, you can move your preferred people just outside your farm, within a few seconds of walking. Combined with the map on the lower screen that tells you everyone's current location, it's easier to reach people and thus build friendships - and it's generally easier to build friendships because the faster farming and plentiful natural materials gives you quicker access to gifts.
Those are some of the more important changes, I feel. Overall, my fiancee is enjoying the game a lot, and she's played quite a few Harvest Moon games before. If you have a GameStop nearby, you might consider picking up a used copy and seeing how you like it before committing yourself.
