Fair enough. Some people say they'd prefer open because they've heard it gives better sound. Generally, open headphones/headset sounding better mostly applies to those at a higher budget.
Choice is pretty slim for open back headsets, even more so at the lower price point. Can't see much other than Roccat Renga. 3* from 31 reviews with more 1* than 5* on a certain website, doesn't inspire much confidence that they are any good.
HyperX Cloud Stinger, is likely a better buy, even though they are closed back. However; while the Stinger carries the HyperX brand, they likely aren't as good as the Cloud I/II, which are based on Takstar headphones; but at this budget they maybe as good as you can get without looking at headphones.
Headphones will offer better sound, but if you really need a microphone, then it's difficult to do any better than the aforementioned headsets, unless you use a separate microphone.
With many headsets, you pay extra for bling and brand names, and even some of the more expensive ones aren't overly good. With cheap headsets, they break, then the user goes and buys another one. Maybe manufacturers see gamers as suckers who will keep buying products that break; otherwise, I don't know why similar price and cheaper headphones offer better quality all round; except minus the microphone of course.
Superlux HD330 are good cheap open headphones with plenty of good comments that look very similar to Beyerdynamic headphones. With delivery they can be had for £35 from a German company. I'd imagine they'd trounce any similar priced headset for sound and build quality.