The good thing about JKTDC is that their hotels can be booked online.....
For Kashmir Valley, I'll say go for JKTDC properties. At Katra you have many hotels and in December you'll off season rates at most of the hotels if you are not going in the last week of December, which is high season there.
In short, at Katra, JKTDC will be expensive. Go for Niharika Complex of Shrine Board.
What difficulty are you facing in planning your Kashmir Valley trip ?
Few suggestions:
1. Is possible stay at A houseboat at Nagin Lake
2. May see Awantipura and Martand ruins....
3. May visit Dood Pathri from Srinagar, very nice meadow by the river Shalin Ganga
4. At Pahalgam, a must visit place is Betab Valley (named so after an old film Betaab was shot here)
5. At Gulmarg, if you want a horse ride, bargain well and decide a price beforehand. Reconfirm per head charges before mounting the horse.
Enjoy the trip......