This poll makes you look like an idiot to any educated music connoisseur. First of all, the bands that you listed are not modern "rock" but rather, crappy pop bands. If you want modern rock, listen to U2, Radiohead, R.E.M., Pearl Jam, etc. These bands have evolved to a point that their "rock", if you will, has become the best being produced today. If you want to go even further, find some stuff thats underground, that many don't know of. As for classic rock, you seem to have some of the best picked at first glance... but what is a lame pop-metal band like Twisted Sister doing amongst the greats like The Beatles, Queen, The Rolling Stones, etc.? That's ridiculous! Secondly, I want to reinforce my friend DaBandito's point that comparison between subgenres is difficult if not impossible, due to the blurred lines between genres and the fact that some bands are simply better than others.
i.e.: (These don't necessarily reflect my views, i'm just trying to get a point accross)
Some would consider Twisted Sister classic rock.
Some would consider R.E.M. modern rock.
R.E.M. > Twisted Sister. Therefore Modern Rock is better.
Now, some would also consider the Beatles classic rock.
Some would also consider Fall Out Boy modern rock.
The Beatles > Fall Out Boy. Therefore, Classic Rock is better.
See how these statements contradict themselves? There's no way to come to a conclusion here unless you define yourself or make your question less specific. The former would be very difficult and the latter would be pointless. Thus, you're screwed.