I think the salient part of your question is "roumours a few years ago".
These days the quality and reliability of almost all CDRs is much improved over those of years ago and even though there may be small technical differences, I doubt that this would be apparent to the general user.
I can't say the same about CDRWs though as I don't know anything about them. Having had some very bad experiences with them in the past, I am not even offering them the chance to redeeem themselves.
So, buy reasonable quality, named brands and you should be OK. If your disks can't be read in some machines, it may well be the machine rather then the disk.