Ron,
They're non-cytopathic, but attenuated.
I'm 30+ years removed from my undergraduate training in microbiology/virology, so can't speak with any authority on how they're 'modified', these days.
In the past, researchers attenuated some viruses by 'running them through' non-target' species, or growing them in non-target origin cell lines - for example (and I'm just making these scenarios up out of thin air), maybe infecting goats with IBR and re-isolating the virus from the goat or growing BVD virus in baby hamster kidney cell line, etc. For some viruses, growing in an unnatural host lessens virulence.
Or, it may be that the vaccine strains were 'discovered' contaminating certain cell lines, and had lost their virulence after multiple passages in cell culture, or were just innately, a less virulent strain from the outset.
It's close to irrefutable that the mlvs elicit a stronger response in most animals, but the inactivated viral vaccines have come a long way over the past 20 years or so. And, in the hands of folks who may not really know what they're doing, or why...the inactivated products may be best, or at least, may do the least harm.