I wrote a big post this morning and lost it- GAH!
I have stayed at both London sites, in a tent with 3 youngish kids.
Crystal Palace
Pros- nearer to the centre of London, and other places in SW London. However, the bus can take its time, we stayed pre East London line so maybe that has helped times? Leafy site with supermarkets, cafes and restaurants 10 mins walk away. No playground but Crystal Palace park is a walk away, slightly annoying that you have to do 3 sides of a square. The camping part is smaller than Abbeywood. The main downside is that it is next to the main road so there is a lot of traffic noise, which being London continues through the night. The noise won't be so much of a bother if in a motorhome/caravan as you would be further away and more sound proofed. The other issue is that the 4 loos and showers are keycode protected and a bit of a pain with young children. There was a family block there but we never got a key, maybe you had to ask?
Abbeywood is further out, and the best way in is by train which is about 10 mins away. The camping field is larger and is car free, with parking on the perimeter. I think they had a few EHU's? The small playground is more suited to under 8's but in sight of the tent field. The facilities are much more family friendly with no keycodes, bigger showers and there was even a family bathroom with a bath. A co-op is 10 mins walk away. I felt ok in the area but then we lived in SE London anyway. The site is much, much quieter at night and from road noise.
I think a lot depends on the ages of your children, Abbeywood is definitely easier if they are younger but CP is slightly nearer the action. I would probably prefer CP, even with the noise but my kids nag for a playground.