This is pure speculation + putting 2 and 2 together (And hopefully getting 4, but we may get a 3 or a 5 somewhere), but;
Pichu's role (In Melee, at least) is a Smaller, Quicker Pikachu with the "class" of a Glass Cannon. Fantastic examples of Glass Cannons in Smash Bros. games would be Mr. Game & Watch (to an extent,) Smash 4's Little Mac and Flash 2's Sandbag, their emphasis being they can hit hard but not necessarily take much punishment themselves for a variety of reasons, be it their lackluster recovery ability (Which is essential in a game like Smash) or their lighter-than-usual weight (Meaning they die much quicker.)

In Flash 2, Pichu has been de-cloned a bit as well as (seemingly) refined in some aspects to further fit both the roles of the "Smaller + Lighter Pikachu" as well as the "Glass Cannon," with his new array of Specials making him a bit more gimmicky than Pikachu.

As comparisons, let's take Pikachu and Pichu's Down and Neutral Specials.
Pikachu's Neutral Special--should i need to re-explain it--travels across the stage in a bouncing fashion, going along walls and usually ending when met with a ledge. Being an electric move, it deals a bit more hitstun than your average move and is great for Zoning.
Pichu's, unlike Pikachu's now travels in it's own unique way. Similar to Luigi's fireball, it "floats" in a specific direction depending on where you use it. Using Neutral Special when Pichu is on the ground causing it to float diagonally up, and using it in the air causes the ball of electricity to go diagonally downwards. This changes the Zoning feature of Pikachu's Neutral Special into a more Trap-like move designed to constrict your opponents movements and let you get in, especially with Pichu's greater speeds.

Pikachu's Down Special--for the sake of explanation--brings a thunderbolt from the sky that does one powerful hit and knocks the opponent sideways, as well as having a powerful hitbox should the thunderbolt collide with Pikachu. This can be useful for catching opponents trying to get back onstage and further hampering their progress, as well as a great "get-off-me" tool should you have the time to use it.
Pichu's has a similar-but-different purpose, as his thunderbolt is not only a Multi-Hit (Instead of one, powerful hit) but also send the opponent directly downwards (Not factoring in Direction Influence--or "Hitstun Shuffling" as Smash 4 would call it) making it useful for not only comboing into the hitbox that Pichu gains when the thunderbolt collides with him (Should they be caught early,) but also being an even more powerful tool offstage as Spiking an opponent usually has much greater results as opposed to sending them horizontally, as a lot of characters in Flash 2 have a much easier time recovering from above/horizontally than from below (Good examples of this would be Sandbag, PAC-MAN and Tails) so sending them downwards has much bigger room for results, and possibly sealing their stock.

Other moves have been changed to refine Pichu's aspects (Such as Up B and Side B going farther distances than Pikachu's, making recovery easier among other purposes) and whilst the Self-Harm mechanic seems quite damaging--pardon the pun--remember that Goku also has this gimmick with his Kaio-Ken x2 mode, which ramps up damage constantly (and at quite the fast rate) as the form is in use instead of just when using certain moves.

Overall, Pichu seems like a riskier version of Pikachu that you can get great rewards out of, provided you learn the ins and outs of him and learn how to hit his Electricity-charged Moves (As those are the ones that damage him, missing it might cause more harm than normal) as well as offering a different playstyle due to his speed and alterations on the aforementioned moves and others.
I could be entirely wrong once 1.0.3 releases, but here's my pepper and salt on the fine dish of speculation whilst we wait.

Y'all motherhubbards didn't know I could science some s*** up, did you

It looks like Pichu's FINALLY becoming the high risk=big rewards character I always wished he was in Melee. Don't get me wrong, I LOVE playing as him in Melee, but the high risk=little reward thing could get pretty frustrating at times, if I'm being honest.

Remember guys, Pika has 64 BAir while Pichu has Melee BAir

I am super worried about his side tilt.
In melee that thing had the tiniest hitbox ever, with a pretty significant amount of lag to boot.