Why will it matter? I know some fans like to play the "big club" top trumps game, but in the modern era do players really give a [Poor language removed]?
It's not really a question of being a bigger club, but if a player has a chance to increase his wage at a club with more ambition, and better prospects of a more successful/enjoyable playing career then they are going to strongly consider it.
I take your point that Everton haven't done a great deal in the PL era, but let's be honest, of all the established current PL clubs, Sunderland have done absolutely nothing of note for a good 16 years when you last finished above us and even then it was only a 7th placed finish. Players will notice that. Of course we're not a glamour club ourselves currently, but we've still achieved European Qualifications in recent memory and played in quite a few semi finals etc. Kone will know that his time at Sunderland in the present era will either be a relegation battle or a 14th/15th placed finish until Moyes can hopefully take you up the league.
I'm not suggesting Kone will see Everton as a huge step up from yourselves or that he will even come this window, but it's pretty obvious from his behaviour that he isn't set on staying at Sunderland. That's just something that happens to clubs like yourselves due your poor performances on the pitch for a long long time. It happened to us in the 90's and 2000's, and even now, if a "current" bigger club with more ambition and better chances of success comes along like Man City, then the player will want to leave.
I have a lot of respect for Sunderland as a club and your fans by the way so I hope you don't take that the wrong way.