Yep, using tools like kprobe2 (on Linux) or Plextools and the popular
Nero CD-DVD Speed (for Windows), is the best way for a home user
to test the quality of a "burn".
But unfortunately only Plextor drives and some LiteOn drives are able to submit the C1 and C2 error counts. But professional test equipment for CD/DVDs costs several thousand dollars/euros, so you can be lucky when you have a drive that supports this nice extra.
When it comes to CD ripping, any ripping tool with sophisticated error detection will tell you whether a rip is going smooth or not. And as Canar said, if an Audio CD is ok, then any CD drive will rip it perfectly. But as many Audio CDs come with a kind of copy-protection that is based on intentional errors, a tolerant CD reader is important.
As I said, if you don't want to test out many drives for yourself, go check out www.cdfreaks.com, it's a community dedicated to everything that has something to do with optical drives, they test blank medias as well as drives.
As for the folks that claim certain kinds of drives are better for this and that than others: it's true to some degree that nowadays there are some drives that are horrible at reading scratched or copy-protected CDs. Whether this was intentional by the manufacturers or whether it's because that today other qualities are more important (speed/burning/support for media formats), I don't know. But it's a fact that there are very good drives out there for reading purposes, and of course those drives will always stand out and be remembered, even when they are out of production... this might also lead to the impression that in the older days there were better drives for Audio CD reading manufactured than today.
Personally I'd rather look out for a "new" drive that's good at burning even the newest media (DVD-RAM might be interesting)
and which is also good at reading CDs/CDDAs/DVDs and maybe HD-DVDs/Bluray, too, instead of having 2 or more drives in my PC or maybe even buying an old piece of junk off from ebay because it is said to be an excellent ripper.