I don't know about Ultimate, but, as far as I know, Pichu doesn't have much that Pikachu doesn't. Below are lists of positives and negatives of Pichu, compared to Pikachu.
- Pichu can wall jump, Pikachu cannot.
- Pichu has a higher traction than Pikachu. (slightly less slippery)
- Pichu has a larger sweetspot hitbox for his U-smash.
- Pichu's D-smash can semi-spike, gives him intangibility frames, and has higher knockback.
- Pichu's U-air can more easily combo into itself with fast fallers.
- Pichu's D-air deals more damage and is stronger.
- Pichu's grab range is slightly larger than Pikachus. (nowhere near as good as the godly grab range of Ness, though)
- Pichu's Skull Bash (side special) can be charged for longer, is a lot more powerful when fully charged, and travels much farther. (this has caused me to lose multiple times)
- Pichu's Agility (up special) can go in a larger variety of directions than Pikachu's Quick Attack.
- All of Pichu's attacks that use electricity cause him to take recoil damage. (F-smash, F-air, D-air, pummel, F-throw, Thunder Jolt (neutral special), Skull Bash (side special), Agility (up special), and Thunder. (down special))
- Pichu runs more slowly than Pikachu.
- Pichu is quite a bit lighter than Pikachu. It will take more knockback, which means it won't survive as long.
- Pichu's attacks are generally weaker.
- Pichu's tilts have shorter reach than Pikachu's.
- Pichu's smash attacks both deal less damage and do not reach as far as Pikachu's.
- Pichu's F-smash can be SDI'd out of before the final hit connects.
- Pichu's U-smash comes out one frame later and the hitbox doesn't last as long as Pikachu's.
- Pichu's D-smash, due to its angle, cannot combo, so it's impossible to rack up damage with it.
- Pichu's U-air doesn't have semi-spiking properties.
- Pichu's F- and B- airs deal less damage than Pikachu's
- Pichu's F- and D- airs give more recoil damage than its other attacks.
- Pichu's Skull Bash has more end lag than Pikachu's
- Pichu's Agility is slower and does not travel as far as Pikachu's Quick Attack. It also does not deal any damage or knockback. (despite giving Pichu recoil damage for using it)
- Pichu's Thunder isn't as powerful as Pikachu's and, due to its multi-hit property, can be SDI'd out of.
I think that the Smash Wiki sums up Pichu pretty well:
> Pichu not only performs significantly worse than Pikachu, but is considered a bottom-tier character and sometimes even referred to as a joke character. Although Pichu is very small, this makes its range very low. It also has a somewhat below-average approach as its only option is Thunder Jolt to use as a projectile while Thunder isn't good either, due to being able to SDI out of the move for being multi-hit. It's also the lightest character in the game which makes it extremely easy to KO, although its small hurtbox makes this somewhat difficult. Arguably one of Pichu's biggest flaw is that it takes recoil damage from its electrical attacks, harming its survivability even more. As a result of its major flaws, it is considered to arguably be the worst clone in the game and overall one of the worst clones in the series.
In the end, the few things that Pichu has that Pikachu doesn't are outweighed by Pichu's many other flaws. I'd personally advise against using Pichu over Pikachu is you're playing competitively, but, if you're just playing for fun, it doesn't matter much. I personally like using Pichu more than I do Pikachu, but that's just my opinion.
TL;DR: Pichu is incapable of taking the Bee Gee's advice.