AA and DLA (now PiP) are essentially the same benefit with AA being for people over 65 and PIP being for people under, with the following exceptions:
Pip is broken out into 2 elements -1 for care and one for mobility, AA does not have a mobility component, just care (presumably because older people are expected to have worse mobility anyway).
however, if you apply before you are 65 and get PIP, the mobility component can carry on. If you are over 65 when you first apply, mobility does not ever come into it.