Not a bad comparison.
According to my TMS era ranking thread, Roddick sits just behind Courier and will likely overtake him pronto.
Purple Rainbows TMS Era (and beyond!) Ranking List!
Courier is way more accomplished than Roddick on clay and at the AO.
Roddick has a much better record at Wimbledon, the US Open and the hardcourt TMS events.
Roddick has also won more overall titles.
If Roddick had been born 2 years earlier, he'd have had a window of opportunity post-Sampras and pre-Federer to snatch a few more slams and we probably wouldn't have this discussion.