Thunder Burst is a pretty good move imo.
It's one of pikachu's best move for punishing ledge get-ups. Thunder burst has better range than the original so it can punish both normal get-up and roll get-up, and if you SH, some get-up attacks. It is one of pika's few moves that hit underneath the stage, and lasts long, so you probably could punish ledgesnaps during the 1 frame of vulnerability. Short hopping into thunder burst alleviates the start-up time basically because you can just jump over some moves, plus the end lag is no big deal if you hit.
I've experimented with all of pikachu's customs and I think at the moment that these are the order of how useful his special moves are from most useful to least useful.
Quick Attack, Heavy Skull Bash, Thunder Jolt, Thunder Wave, Quick Feet, Thunder Burst, Skull Bash, Meteor Quick Attack, Thunder Shock, Distant Thunder, Shocking Skull Bash.
Thunder Wave and Quick Feet are the only two that I think actually are better than their defaults in some cases. And heavy skull bash in all cases of course. Shocking Skull Bash is the only custom I feel that is downright useless (but it has a nice visual effect D: ). If any customs needed to be tested to see potential it would be Quick Feet, Meteor Quick Attack, then Thunder wave, and maybe Thunder Shock.
edit: it seems the start-up time for Meteor QA was lowered from 1.04. It might be slightly better than I thought since the start-up time was a huge issue before. I honestly should have done all of my testing on the wii u version :/.