Arsenal were a team struggling to compete for the league title and having a constant battle to finish in the top 4 at the time, RVP left for the title winners who had been Champions League finalists the season before. I’m sure he received a nice pay rise as well but there were football reasons behind it.
I can’t really speak for Tiago but he left to join the best team in Europe who had recently appointed a manager who had been a mentor to him. I suspect that as with any transfer where the player is joining a ‘better’ team a pay-rise will have been given as he can’t have been on a great wage with his contract at Barca.
In terms of how Man Utd would be able to recruit a better standard of player than they currently have I’m sure a tour of the stadium and a quick look in the trophy cabinet will have a say. They are still one of the biggest clubs in the world and will still pay players top money. If they do manage to get Champions League qualification which still isn’t out of the question for this season they’ll have a fine standing with potential transfer targets