There are a hell lot of bugs in AndEngine...
i had first the same dilemma of choosing one thing over other but my options include libgdx,andengine and cocos2dx...
Though libgdx is a framework but its the most powerfull of them all and you can go very deep in the code (u might create some extraordinary events)...but for a beginner like me thats a tough one as i have no experience of game programming (also the kind of easy docu given at its site allures you to use it but after a while when you want to create something of your own you are puzzled)..
But the best performance is guranteed !!
Next comes the AndEngine ..excellent work doen by Nicolas..but alas the bug count is ever rising and there are not consistent results around the devices..its one of the major drawback..you can avoid bugs but when performance is hitted hard you have no option but to leave it !!
Cocos2d-x(this is what AndEngine without bugs and good-performance would be like in the future)..
but the only drawback with cocos is the programming on not-a-mac OS...you dont have the usual code completion and tiny-miny features which are programmers essentials these days..but for performance and bug-resistent coding we have a runner-up to libgdx !!