If you live in somewhere like Aston Clinton or Wing and you drive to get to the station, then it's a no brainer to go from Tring. The trains are faster and there are more of them, and the car park is bigger. Train standards are about the same, I don't see much difference in comfort between the 165s and the 350/2s, and definitely not with the 321s.
If you're having to use public transport, the sensible choice would be Aylesbury, simply to avoid that two mile walk from Tring town centre.
I don't see what they could do to speed up the Aylesbury trains, the main issue is the number of stops the trains make in Buckinghamshire. Take out a Wendover stop and there'd be war on.
You used to be able to get joint-availability season tickets, valid at both Aylesbury and Haddenham, do Chiltern still do these?