Following on to The_Banking_Scot's feedback, Old Town is much more compact and immediately walkable of the two stops you mentioned. If you are interested in more of the early California settlement context as well as different places to easily walk to for lunch, Old Town is good for that. Taking the trolley from there, you can head east toward Mission Valley - or you could take the trolley from there South to Downtown and, after walking around there, pick up Amtrak from there heading back north.

The Santa Fe depot downtown is more current urban, next to various piers and San Diego Bay. It is much more spread out but there's far more there - a few blocks north is Little Italy, going east you'll hit Horton Plaza and its mall, heading south is Seaport Village and the Marina, taking the trolley Southeast, you'll be between the Convention Center and the Gaslamp District.

The only other comments I'll make are: it's all touristy and fun; if you go on some weekends, you're gonna have a lot of other folks on any mode of transportation (train, trolley, bus, car, etc.) to contend with; if there's a baseball game and/or weekends, it may be insanely busy in the Gaslamp District.

David