Blu Rays do look better...but only if you have the right setup. The right cables, a big enough TV, the right distance between yourself and the TV, good enough eyesight.
If you're just watching these movies on a monitor the size of a laptop or so, I think the difference MIGHT be noticeable if you compared them side by side...but it'd be negligible. It's only when you start to blow things up on a bigger sized TV that you start to notice the difference.
Personally, I'm perfectly fine with 480p/DVD quality definition, myself. Anything BELOW that is a little rough, though. 720p IS better, but anything above that is...barely noticeable to my eyes, but I have poor vision and only a medium-sized TV. I can see the movie fine, so meh? And some things actually look WORSE on Blu Ray, but that's really mostly down to badly done transfers of older stuff.
So, if you're saving money by getting the DVD version and it doesn't bother you, who am I to say you shouldn't do it? Blu Ray MIGHT be a little more future proof, though? Eventually, they might stop supporting DVDs, even if there's no real reason they should, if only for the money. But, even then, the industry REALLY wants 4K to be the new standard, even though...I feel like you need a HUGE TV to tell the difference between a Blu Ray and a 4K disc. There are people who really want that maximum theater-like experience at home...but, speaking personally, I don't really need it.