External burners can get out of alignment pretty quickly. It sounds like your read laser is misaligned so that what is causing the difference in what you can burn or read. The write laser is a much stronger pulse which helps it to make up for small misalignment problems that when the drive reads with a smaller pulse it isn't able to make up the misalignment.
If you want to keep the drive external you can always pull out the current drive and use a new on in the same case. Just make sure when you buy a new one that you check and see if the current case accepts a SATA or IDE drive.
While shopping for a new drive the new NEC's are real nice drives. LG is also making some nice drives but only for certain models.
Check out
http://www.cdfreaks.com/ for some real intensive reports and reviews on current drives.