For the purpose of this question, I am going to look at the Red from Pokemon Origins.
The answer to this question is simply impossible because both these characters belong to alternate Universes.
One key difference is the lack of a regional league in Red's Universe compared to that of Ash's.
This could mean one of two things.
1) The Elite four in Ash's universe are considerably stronger and there is a lot more competition. Hence, there is a regional league to select the winner who challenges the elite four.
2) The Gym leaders in Red's Universe are far stronger than the anime versions. Hence, it is almost impossible for the regular challenger to collect all 8 pages and only the truly elite talented trainers like Red and Blue end up collecting all the badges.
Taking this into consideration, one could easily argue one is better than the other using one of the above assumptions.
That said, to keep it fair to both Red and Ash, let us assume that all the Gym Leaders/ Elite Four in the anime and the Games are of equal levels of strength.
Taking this into consideration, Red would already be far above Ash's level of strength. Ash is still far from coming close to the level of an elite four member.
In the Red Universe, Blue was someone who was much stronger than the elite four and Red managed to defeat both the Elite four and Blue putting him far above Ash's level already.
To add to that, while the Origin's Mewtwo could be argued to be weaker than the Anime Mewtwo, we can look at it in a more simpler way.
Mewtwo was >>>> Blue who is a champion tier trainer and this is true even in the anime, where Mewtwo is definitely stronger than the likes of Cynthia, Diantha and even Leon. It's one of those special legendary Pokemon > Champion tier.
Red is a special champion who actually defeated this Mewtwo and captured it which is again a very impressive feat.
Based of all these feats, Red is a far superior trainer than Ash. Even if you look at achievements, none of Ash's achievements come close to beating an Elite Four/ Regional Champion level of achievement and he has not captured or defeated a Special Legendary Pokemon by himself, which is stronger than Regional Champion tier.
Edit:
Claiming Ash is stronger than Red would imply, the Elite four in the Origin's Universe are weaker than regular trainers in the anime Universe.
This seems like too harsh of an assumption to make to simply try to argue Ash is better than Red.
If Ash does enter the Master Class, beats elite four members/ regional champions, that would definitely be something noteworthy that would greatly affect Ash's standing.
Finally, another key point I forgot to discuss, is the time period. Red accomplished something much superior in the fraction of the time Ash has taken and the latter isn't even close to the same level of achievement. So even if Ash does become the PWC. There will always be the argument that if Red had the same level of time to train after becoming Kanto's champion, he would still be far superior to Ash.
If Elite four Lance was capable of becoming the second strongest trainer in the world, then someone like Red (Who was far stronger with much greater potential), should be able to achieve a lot more.