The surface is rougher, which provides a scratchy sound if you do not have good flesh nail contact and technique. People say they are noisy, but that is not entirely true.
Digging into the string is easier, and playing with flesh really does work good. If you have a perfectly filed ramp on the nail, which has the right amount of flesh, the rectified, have a tactile feel that is more solid and less slippery, this is a preference that works good for many.
Then there is the crowd who does not care for them. D Addario Pro Arte rectified trebles still have the same tonal characteristics as the standard line, but the difference is a personal preference.
The Savarez 520 R series of strings is different in that they are wound, where the D Addario is simply machine ground to a rougher texture.
I personally like the Savarez, but some say they are noisy and awful. What I don't like is Savarez pricing.
As for tone, I think you can coax the same tones from standard or rectified, but there is a different feel and connection to rectified strings.