Will she wear it all the time? Self winding watches are not great if they get the chance to run down.
The battery powered one is likely to keep time better, be cheaper, and not run down if left on the dresser for a while. The only real downside is a battery change every few years. But the automatic is so much cooler, especially if you can look inside and spend a while figuring out how it all works. Only you know whether she’ll appreciate the coolness or not.
Someone who is likely to appreciate a mechanical automatic movement (that is will wear or wind them daily, puts up with the crap time keeping and generally cares about the mechanism) has probably already got one.
What I really like is a sub-second movement on the second hand. Mine goes in 200 ms intervals. It’s great.