I haven't played many of the Harvest Moon incarnations, but I loved the original on super nintendo and the one for N64. In Harvest Moon you basically inherit a farm and take it from run down to lucrative. You plant crops and water them, you can raise livestock like cows and chickens. You can buy upgrades to your house and you court a local lady and can eventually marry one of them. There are also holidays and various things to find and places to play. It's a great game but its not for everyone.
Animal Crossing on the gamecube sold alot of copies because it was a novel idea. Basically you are a member of a small village and you get to know the residents and they give you stuff for your house. I didn't play the game much but the huge deal about it was that time in the game relies on time in real life. So if you get up early to play at like 6 in the morning the villagers might be doing exercises or such things. If you play late at night people will be asleep. I didn't play too much so not too sure what else is in the game but it is mostly about collecting things from the villagers. Someone else can prolly say more.
I'd suggest harvest moon over animal crossing personally.