For computer use they are not really any different. It's the remanent of a format war that was resolved by everything just supporting both.
If you're burning DVD video discs to play in a standalone DVD player, the particular player may have more or less issues with one type of disc. I never do this, so I'm not really up to speed on it, but in the early days, people reported various problems. I think all reasonably new players read recorded discs ok.
What you really want to be careful is which particular discs you buy for your burner. Different burners work better or worse with different brands and speeds of disc. It might just mean you make coasters more often, but it can also affect the disc's readability in other devices. It's best to check compatibility before you buy a bunch of them. You can read user reviews
here, on videohelp.com. Make sure to check the details and look at what burner people are reporting works good or bad. Pay special attention to your brand and model.
It's also normally better to buy discs online rather than in stores to avoid getting ripped off. I normally buy all of them from meritline.com (for the last 8 years). Taiyo Yuden is generally believed to produce the best discs. Since they have gotten a lot cheaper in recent years, I just buy those.