The physical strain stays exactly the same - a burpee is a burpee, whether you do it in 1995 or today! Your body doesn't know the difference between a DVD from back then and a YouTube video. I've still got old workout videos at home, and honestly, when I dig them out, I don't notice any difference compared to newer stuff. The next day is just as sore!
But the practical side of things definitely matters - and your friend has a point there. YouTube just gives you incredibly more flexibility. You can pause, skip ahead, rewatch a part without having to start the DVD over. And if a video doesn't work for you, hundreds of alternatives are just a click away instead of being stuck with one trainer. Plus, newer videos sometimes take newer findings about joint care and stuff into account, even if the basic movement patterns stay similar.
My tip? Keep using the DVDs if you like the program and it works for you! But for the future, I'd also suggest exploring YouTube - not because the old stuff suddenly got bad, but because you can train more flexibly that way and don't always need the same trainer.