Has your daughter expressed an interest in one instrument over the other? If she has, I'd recommend going with her interest. It might translate to more enjoyment on her part, which in turn would (theoretically) translate towards a greater willingness to practice.
One thought about the violin: I began playing when I was seven years old. It can be painful to play the violin until your fingers develop calluses. The strings can cut and can cause blistering. I think that most teachers would be careful to limit the finger work with such a young child, but it's worth discussing with a teacher, as I could see a 4-year old losing interest in the violin for this reason.
I'm not sure if there's a similar problem to playing the piano, but certainly that would be something I would want to find out about.
Don't mean to be discouraging at all- playing the violin was wonderful for me, and the benefits to playing music are enormous. I enjoyed playing as a child, and the whole finger callusing issue wasn't insurmountable by any means. Just something to factor into your decision making.
Good luck!
M.