Hi Niels,
The Panamanian "summer" (end of December until early April) is usually considered to be the best season. It is also called the dry season, that's mostly why. Less chance of rain during the day, less humid feeling in general, and less muddy conditions on the trails.
Upsides are the presence of North-American migrants in breeding plumage, and, especially by the end of the dry season, the dry leaves on the ground that make it a bit easier to spot ground-dwelling birds without the use of tape or the need to hear them call. I found Streak-chested (Spectacled) Antpitta twice on Pipeline Road during the dry season without tape and without the bird ever calling once.
Downsides are higher prices everywhere, and generally a bit less flowers (my personal impression), which may make finding hummingbirds in the wild a bit tougher. Feeders are the answer to that one up to a certain level.
So if you're willing to spend a bit more, February and March would be the best time. But rest assured, birding can be great any time of the year in Panama!!
Regards,
Cedric