S.F.
I think 12" is too small for a 4 year old. I would go with the 16". Coming from a trike, it is going to take her a little time to adjust to a two wheeler with training wheels. If you have a flat enough driveway, have her practice steering and stopping there for a few days before you go for any bike rides. That way she will be more comfortable.
My daughter turned 4 in February and is on a 16" bike. Which she can ride great and is very comfortable on. She started off on a 12" bike last summer when she was 3.