Ash vs Paul #1
Ash would've won this if Pikachu wasn't nerfed but Paul let Pikachu attack first by letting it use Thunderbolt on Elekid on purpose to boost it's attacks.In the Starly vs Starly bout Paul pointed out to Ash that he figured out his battle style.Paul also told Ash that he made poor choice in attacks by having Aipom use Focus Punch but Paul countered it with Flame Wheel.
Ash vs Paul #2
Paul deserved to win,Chimchar got stronger,faster and learned the move Dig which helped it get the W over Turtwig.
Ash vs Paul #3
Paul had stronger pokemon but the battle wasn't finished due to Chimchar's Hax Blaze being out of control.
Ash vs Paul #4
Paul deserved this one,Ash's Grotle was weaker than Honchkrow and Ash didn't realize that it lost speed due to the increase in it's size.
Ash vs Paul #5
Honchkrow was stronger than Staraptor but Staraptor won the pokeringer due to knocking the ring out of Honchkrow's mouth at the last second.
Ash vs Paul #6
Paul deserved to win this one,he prepared himself and trained his pokemon hard in 10 days before his battle with Ash at Lake Acuity.Ash made a few mistakes in this one like not switching properly and keeping his pokemon out instead of returning them.Even if Pikachu wasn't nerfed Paul still would've won,the yellow mouse isn't sweeping through Electabuzz,Honchkrow,Magmortar and Torterra by itself.
Ash vs Paul #7
Ash won but barley,both him and Paul could've used stronger pokemon,if they did Ash of course would win using his bigger juggernauts but more than likely Paul has other reserves that we never got to see on screen.He didn't earn 8 badges and compete at the Hoenn,Johto and Kanto leagues using only Torterra,Nidoking,Hariyama,Murkrow and Weavile.
------------------------------------------------------
Overall I'd say Ash lost due to not using pokemon like Charizard,Snorlax and Sceptile or Pikachu being nerfed.But besides all of that the battles him and Paul had Paul was in control and was consistently battling better from a skill standpoint,he's also naturally more intelligent than Ash too.This is helped Ash improve as a trainer.
XY Ash improved in areas that he was struggling in from DP but he still made silly mistakes in battle which is something Paul would not do,the guy is brutally efficient.One of the biggest XY fans on here even admitted that Paul was more skilled.