I would agree with most of what has been said here. I have travelled/boated in Guatamala and Honduras in January. Cheaper to travel but harder to get around.
Costa Rica and Panama are much easier to get around but more expensive. They also have the added benefit of better water/food quality so there is less chance of getting sick simply from eating.
Specific to Panama, January is the early dry season. The bigger watersheds will still have water, but the creeks on the Pacific side are usually too low to paddle. All the easy access is on the Pacific side. If you are into remote/multi-day rivers, there are a bunch on the Carribean side that take at least 2 days to get to a put-in as well as some on the Pacific side. You can easily spend 4 days on the Chiriqui Viejo on the Pacific side, either as day trips or overnights (normally class 3/4 in the dry season).
If you are traveling by yourself and need paddling partners, Costa Rica probably is a better destination (Panama's rivers are VERY uncrowded).
Let me know if you need any more information on Panama.
John Miller, Boquete Outdoor Adventures