We had this dilemma and went with a Vtech innotab - very similar to the leappad but it has a memory slot so you can load on your own movies and music onto so you're not locked into the leapfrog material. We've been very happy with it. We also have a tablet but DD uses 'her' tablet more than the regular tablet.
its very child friendly, pretty much indestructible. She can't get online with it, cant delete or remove any of the games or apps. you get a heap of free apps and they're not overly expensive to buy books, games, etc.
Rechargeable batteries last about 8 hours so I just cycle 2 lots through it.
Really happy with our decision but as DD is only 3 she only really uses it for the movies and music. She's not really into the games much. Target has been throwing them out for $44 each (I brought 4 of them!).