I used to be a Notts AA member til about 9 years ago and fished both places. Assuming they haven't changed much in that time -
I fished Oldmoor regularly for a while - it's highly stocked and the carp are mainly to low doubles but a few a bit bigger. The biggest was rumoured to be a low twenty when I used to fish it, but my pb from there was 16 and a half. As Nottscarper says, definitely a runs water - margins and island best. I also used to catch a lot off the top.
I only fished Bestwood a couple of times, just before a time when I stopped fishing for about 5 years. Number 2 was the main carp lake (bivvies & buzzers allowed). Did 2 night sessions on there and had 6 fish each session, biggest 21lb, both times fishing near the island with PVA bags of whiskey boilies and pellets. At that time the carp supposedly went up to about mid 20s. I couldn't really comment authoritively on features on the basis of only a couple of sessions, but wasn't aware of any major underwater features on number 2. It's a nice looking place, but not really my type of thing now - mainly because (again assuming it's as it used to be back then) it's too busy for my tastes.