At the price of the J1/J2 the market is absolutely rammed with really good cameras all of which will take great shots and offer the choice of going down the manual route as opposed to point'nshoot. Sorry that doesn't make things clearer but after that it's personal choice and what you can take from the opinions of those that review these things like science projects.
Questions to ask yourself: will she use it? Will she want a system camera with interchangeable lenses? something that is truly pocketable? monster zoom length?
Best of luck, it's more fun choosing these things for yourself ;)