I have about 25 years experience in fly fishing for pike, and a bit less than that in tying pike flies. I'm happy to help if anyone needs advice.
I have fly fished for carp as well, but not seriously. As well as catching them on dog biscuit imitations made from clipped deer hair I have also caught them on trout flies (mainly nymphs). I think this is more challenging but ultimately more like 'real' fly fishing. The water I usually fish is shallow and the water clarity is poor because the carp churn up the bottom looking for food so I tend to try and cast towards visible signs of carp moving or feeding rather than fishing blind for them.
One thing I would add, and please forgive me if I'm stating the obvious, is the need for a rod with a decent amount of backbone. I have a couple of 10 wt. rods that are only 8 ft. long and have some serious lifting power (they were bought for fly fishing for big pike from a boat) . Carp will run a long way - and fast, especially in shallow water, which is great fun, but there's no point doing the difficult bit in hooking them, only to lose them through not being able to apply enough pressure to keep the hook hold secure at distance.