Robio,
Sorry if I wasn't being perfectly clear. I'll try again

[1] As far as
file systems go [UDF vs. CDFS] both your systems should be able to read CDFS without problems. It's pretty universal in PCs. I don't think your problem has anything to do with Direct CD at all, since you're not using it to read or write the CDFS discs.
[2] As far as
burnable discs go, early CD drives and their old CDs were a bit insensitive so reading and writing were slow. Advances in the technology have brought changes in the dyes used in burnable discs to allow faster reading and writing, but some of the older drives don't much like the newer, lighter colored dyes. Some of the older dyes were very dark blue, whereas some of the newer ones are very light golden colored.
Your laptop must have a few years on it if it's running Direct CD 5, and I'm suggesting that it is having trouble reading the disc written on your Vista desktop. The suggestion to try a blank with a darker dye, or to try a RW disc, and a slower burning speed, are all things which have helped me some times in the past and
might help you. There are no guarantees here though, and I have had to replace the old drives on occasion when nothing else helps.
I hope this is a bit clearer, but ask more if you need to.
Cheers,
Brendon