My dad's PC has DirectCD, I have InCD. They didn't read each others discs untill I updated my version of InCD.
I can't remember which version it was I updated to, but it was well over a year ago, probably nearer 2 years, so assumming it is current versions of both I suspect it will be OK....
However... You should be aware that, contrary to popular belief, InCD is NOT "part of Nero"... it is a sister programme and has to be installed seperately. If you are happy with DirectCD there is no reason why you should not use this and Nero.
You should not, though, have both InCD and DirectCD installed and runnning together. They are likely to conflict with one another, fighting for control of the CDRW.
I hope this helps,