I think the comparison is difficult, because Shearer was a #9, and Rooney has been more of a jack of all trades.
Shearer was an exceptional striker but Rooney, at his best, was also an exceptional player. Shearer was lethal anywhere within 20-30 metres of goal but Rooney, at his best, arguably had more to his game.
At his best Wayne Rooney was capable of accelerating past players, committing defenders, making space for others. When he picked up the ball there was a sense of excitement about what he might do. Even if he wasn't scoring he was a threat, he could make things happen.
I remember back in 2011-12, the 3-3 with Chelsea. Rooney was garbage first half but in the second half he drove us forward to get us back into the game. He just doesn't do that sort of thing anymore. I mean, look, I'm referencing a game that was five seasons ago now...
Its easy to forget how good Rooney was, especially in 2009/10. Shearer was more consistent throughout his career, as an all round player Rooney was arguably better though. At least at his best. Nowadays its hard to make the case that Rooney could start for any of the top teams in England, either as a forward or a midfielder.