There is no comparison between Walcott and Wilshere over than playing for Arsenal.
Wilshere, much like Barkley, has been massively overrated by English fans because his every once in a while abiltiy to "run at" players and look Spanish every once in a while. But both Wilshere and Barkley have a complete lack of a footballing IQ, which is something you cannnot overcome in the middle of the park. Despite all that, would he be useful on a free? Sure. But he'd likely be on big wages, and, probably more problematic, he's been coddled so long as an English wonderboy that his ego may not be able to handle fighting for his place in a squad like lowly Everton - he'd expect to be first on the team sheet here - something I'm not prepared to give him.
Walcott had long productive patches in the Arsenal team, but he either got derailed by 1) injury, or 2) wanting to believe he was a true number 9. I think he now realizes he's not a number 9 and we're reaping the benefits of that now. But the injuries with him are always a concern.
A lot of my mates are Arsenal supporters and have been for a long time. Every one to a man wished Walcott well coming here and said as long as he stays healthy he'll be a good player for you. As for Wilshere, feelings are mixed, and some would fly to London to drive him up to Finch Farm themselves.