More in-depth analysis of what one has which other doesn't:
Raichu has:
- Very slight size, reach and weight advantage
- Mind Manipulation
- Social Influencing of other type
- Minor Luck Manipulation
- Minor Weather Manipulation
- Afterimage Creation
- Minor Berserk Mode
- Minor Light Manipulation
Ash's Pikachu has:
- AP advantage
- LS advantage
- Social Influencing of other type
- Stronger Electricity Manipulation
- Metal Manipulation
- Danmaku
- Limited Thread Manipulation (Via Electroweb)
- Barrier Creation (via Electroweb)
AP advantage is exactly how big? And AP advantage is only in electric powers or also in physical power?
Well, Ash's Pikachu has habit of waiving the rules and ignoring Immunities and Abilities. However as stated in assumptions, "Raichu can waive the rules just as much as Ash's Pikachu can" - so Raichu could counter it by waiving the rules himself. As such, their munchkin-ness nullifies each-other.
I would also point out that 'chus aren't absolutely immune to electricity. There were times where Ash's Pikachu was overloaded with electricity by Team Rocket and got sick; Raichu needs to drain excessive electricity into the ground, becoming stressed if they can't. And since they're fighting, the best place to drain energy into is the opponent - by launching electric attack at him - causing him to get overfilled and launch attack back; which results in increasingly more powerful discharges being sent to each-other, until someone "short-circuits". Having extra charge makes electric Pokemon stronger and faster, but too much makes it weaker than normal; i don't remember what exactly happens when Electric-type "short-circuits", but that may result in statistics decrease, being unable to use electric attacks, or incapacitation.
As such, the second possible strategy is for Pikachu and Raichu to essentially force-feed each-other with electricity until someone can't hold it anymore and incaps. The first is, again, bonking each-other with tails. Since Pikachu has higher AP, indicating stronger discharges, he can hold more than Raichu before "shorting out" - that is, if Pikachu and Raichu just bear-hug each-other and discharge, Raichu will incap first. If they bonk, then Pikachu can hit harder and shove/push Raichu around, and i don't think that extra length of Raichu's tail can fully compensate it.
Since Pikachu can hold more electricity while Raichu has slightly larger size and reach, the bonking wincon is slightly better for Raichu while overcharging wincon is slightly better for Pikachu. But both wincons are possible for either 'chu.
And also, extra LS means that Pikachu can get and maintain grapple at Raichu - in which case, unless Pikachu lets him go, Raichu's only options are weak attacks with limbs (weaker and shorter than tail) or discharging into Pikachu. The best option for Pikachu is to grab Raichu's tail - as that would prevent Raichu from discharging into ground, prevent Raichu from using his tail to bonk and allow Pikachu to nearly constantly be directly behind Raichu, where he's very difficult to reach. And said Raichu's tail is often at Pikachu's arms reach, since it's the very body part Raichu tries to bonk him with. The fact that Raichu's tail is on high voltage is mostly irrelevant for Pikachu, since his electricity capacity is higher.
So... If Pikachu and Raichu attack each-other with electrical attacks, they keep circling electricity back-and-forth until Raichu "short-circuits" and incaps, since Raichu can hold less electricity. If Pikachu and Raichu attack each-other physically, then fight would result in Pikachu swinging Raichu around by his own tail like flail and hit things with Raichu until Raichu faints, since Raichu has not enough LS to break free - and even barring that, Pikachu just hits harder.
So, i vote Pikachu. And count it.
