You'll hear differing opinions because they're very close. Personally I've thought Pearson had a certain x-factor from the first time I ever saw him. A sort of instant 'this kid will make it' feeling that I don't remember having about an English youngster at such a young age since Wilshere (and before him, since Rooney). His steady progress since then has had a sort of inevitability about it. Rothwell, by comparison, seems to have made dramatic steps forward quite recently. He's probably as good on paper, but I still think if I had to choose one Pearson has that extra little spark. He's mentally the strongest youngster I can remember watching. Sometimes he drags us into games purely by force of will.
It's hard to compare them though because they're so complementary. They're both generally at their best when they partner one another in midfield. Their different qualities fit together very nicely, and they're always on the same wavelength.
If you can find compilations for either player from the semi-final against Liverpool last season, that was a great example. I lost count of the number of times Rothwell was there to go into a tackle or stretch to make an interception, and then Pearson seemed to materialise out of nowhere to scoop up the loose ball before anyone else composed themselves, and ping off a pass to set another attack in motion. And every time Rothwell drove forwards, starting an attack, and Liverpool got the ball clear, Pearson would be in the right place at the right time to take the ball straight back and recycle it into another attack.
Either way, I'd put money on Pearson being the first to get serious chances, because he's the more defensive of the two, and thus more what we need based on our current resources. Rothwell is a lot like Herrera in role and position.