Hi guys, Pikachu main here to help out and give some input for you.
For one thing ESAM believes Pikachu's better stages are Battlefield and Lylat so I would avoid those (mostly for the crazy QAC shenanigans lol).
Two, Pikachu's T-Jolt is equally annoying as needles imo and their movement options are about equal. I suggest playing whichever play-style you are more comfortable with (aggressive or defensive) because neither character can really force the other to approach.
Three, really avoid that up-tilt of Pikachu. It usually can combo for 30ish% or more if follow ups connect. Also d-tilt to trip to grab then whatever is another combo you might see. The d-tilt has good range and helps Pikachu's footsie game.
Four, always DI the throws away from Pikachu if possible. Up throw to sweet spot thunder is potent but avoidable.
Five, do not expect to see many down smashes or normal skull bashes from good Pikachu players. Those moves are too slow and conditional.
Six, your recovery is good enough to make Pikachu's edge guard game on you very difficult. If you recover well, Pikachu will not have much of a chance to gimp you, and you will survive very long against him as Pikachu has a hard time getting KO's too.
Seven, beware the thunder and n-air as combo breakers.
Eight, if Pikachu is under you, he has the advantage because Sheik's d-air is not very good compared to the mad juggler that is Pikachu's u-air.
Lastly, that picture is pretty hilarious but misses out on the awesome adorableness that is Pikachu! See!