Bursts do the best shield damage/energy in terms of overall usability - they are close to beams but have much better energy usage. (am talking large here, I don't think C2 burst has been added to the list yet and i don't really think C1 weapon comparisons are worth that much)
Their armour pen sucks though, and is really noticeable if you try to hit subsystems with them I believe this is why they are not used (or certainly is the reason I stopped using them).
You know I think I noticed that when I was using bursts. I thought that pulses target subsystems more reliably - but I thought I might be imagining it.
Still the C3 Fixed Beam is good for melting shields fast, especially important against bigger ships that are tougher but easier to hit. The pulse (plus autocannons) seem to do the job in terms of subsystems.