Didcot looks rather unlovely compared to Abingdon, but it has a lot more going for it in my humble opinion!
Abingdon is pretty and has a Waitrose and a few nice independent shops and that's about it...
By contrast, starting with public transport, Didcot has a mainline station, Abingdon hasn't. You can be in London Paddington in 45 minutes from Didcot, and Reading and Oxford are 10 minutes away.
There is a cinema in Didcot, there isn't in Abingdon. In Didcot there is also a fantastic arts centre, Cornerstone, with a theatre that has a great programme, an art gallery with really good exhibitions, and courses for adults and children.
The shopping area is thriving, unlike Abingdon's which is slowly dying.
The swimming pool is one that has a flume and wave sessions, great for children.
I can't tell you much about toddler groups and the like as my DCs are too old for them but I know there is a children's centre and some good playgrounds.
Housing is also a lot more expensive in Abingdon, at least it was the last time I looked. You can get a lot more space in Didcot than in Abingdon.
Also the traffic and parking are hideous in Abingdon.
The villages are lovely, but there is not much going on there, and if you can't/won't drive then you have to rely on slow and expensive bus (coming from London the price of bus fares was a bit of a shock!).
Wallingford is also really lovely-looking, and has an independant cinema, a theatre, nice shops, but no mainline station.
Hope that helps you to narrow it down! 