In the actual game, Jigglypuff does bugger all exceptional. She's not supposed to, she's just another second evolutionary stage Pokemon. Hell, Jigglypuff's most well known move, Sing, is far from exclusive to her. Pikachu is in the same boat, actually. Thunderbolt is anything but Pikachu's signature move, and Volt Tackle is the last thing your Pikachu needs. Oh, goodie, it's a physical Electric move with 120 base power and perfect accuracy, and it has a chance to paralyze! Too bad you also take 1/3 of the damage you just dealt and with Pikachu's less than optimal HP stat and wet paperbag-like defences, you will always set yourself up to death or even just outright kill yourself using it. Pikachu's bad Attack stat also ensures this isn't even gonna deal that much damage, but even then, if you use this move against a Lapras at full health, for example, you'll likely not kill it, and then lose 3/4 of your HP in the process.
Why am I even saying this? If you use Pikachu, you obviously don't care about competitive Pokemon battling.
...Well, if Smash stayed true to canon, Pikachu and Jigglypuff probably would be one of the worst characters in the game, and Pikachu would take ridiculous amounts of damage if he used Volt Tackle, specially if he got plenty of KOs with it.