There's load of threads out there on this, but they tend to get lost in a load of chat about the relative merits of specific boards and their surfers
Im gonna split this a bit - popouts, epoxys and custom boards.
Popouts, like BICs NSPs etc are big and heavy and not particularly sophisticated. But they're perfect for learnging on because they're tough and built for the job of learning. And they can be surfed to a high standard if you're good.
Epoxys - that is, high performance "pop-outs" like surftechs. They're very light, and very strong, and the model that you're buying would almost certainly be a popular 'good' board (whether it be long, short, fish, or whatever). Downsides are that they're expensive, you cant choose exactly what you want, and they are very stiff which can make them feel a bit peculiar.
Customs - the biggest and bestest thing is that you can have a board made exactly how you want and it'll be unique to you. And if you chat to the shaper he'll be able to tell you what you need. The only real downside to a custom board is that they can be fragile and get damaged quite easily.