No sane person who supported OG Xbox/360 would support the corporation who destroyed the brand and its mascot Master Chief's game.
Also the multiplatform thing was not always sunshine in Xbox. The 6th gen GTA games were superior on PS2.
Many Japanese games like Tales of Vesperia and Eternal Sonata got extra content in PS3. PS3 versions of many games like FF XIII and Catherine had better cutscenes as they were compressed in 360. GTA V looked better on PS3 due to superior textures.
Splinter Cell Blacklist had superior textures on the PS3 disc than 360 disc. For 360 you had to install HD textures DLC to have textures as good as PS3. Now that 360 online is gone, you have the superior version in PS3 only.
It was all on case by case basis.