I have a 1963 and a 2006 pre-Remington 39A with a cross-bolt safety. Both are great rifles, and my experience has been the newer one is just as reliable and accurate as the older one.
Regarding new 39As, I understand QC slipped as Remington took over, but I've been reading some reports that suggest QC is coming back up. Best to check out the specific rifle you're interesting in in person, then.