I happen to have owned both a set of the Astro A40s and the PC37X. The PC37X are better in just about every way, but I think there is a little too much hate for the Astros and especially their Mixamp.
Astro A40 + Mixamp: These headphones are not very good without the mixamp. The Mixamp hugely improves the headphones and makes them actually not a bad headset for gaming, especially if you are playing competitive online games. They are pretty comfortable as long as you don't have exceptionally big ears. These really need the Mixamp though, without an EQ these are really hard to recommend at all. If you are willing to put in the time, the Mixamp is actually pretty good. This isn't anything near what a good EQ or dedicated headphone amp will do, but it's honestly a pretty nifty device. Both regular audio and communication audio get passed over the same usb cable, which also powers the device (from a convenience prospective this is freaking awesome). You also can hot mix between how much game audio or how much communication audio you are getting in your headset, and you will also be getting your mic fed back into the headphones as well to make sure you're not too loud or popping into the mic, as well as you can mix in an aux device to listen to music or something. It also has Dolby 5.1 virtual surround built in which you can toggle on and off, honestly this is hit or miss depending on the game. Finally it also supports optical input so you can plug it into your TV and use it with a console. It also has some unique tournament and streaming features but most people won't make use of those. There aren't many devices in this product category, Sennheiser GSX 1200 PRO and the Creative Labs X7 are both more expensive but are overall better products with similar features. Through all this though, you need to put in work to design and EQ that you will like for your headphones, and even then it won't sound as good as if you were to use a real dedicated amp, even a cheap one. The Astro A40 mic is alright, it's serviceable and better than the average gaming headset mic, but it's not much. Quality wise, the headphones are a mixed bag, the plastic feels cheap but while wearing them they don't feel bad, I did have some issues with the low-ends in my headphone though, I think something is loose but they have been through a lot over the years so that also could be my fault.
Senn PC37X: These alone do not have any Mixamp bundle, no virtual surround, no software out of the box, they are just headphones, and as headphones these are really great. Easily my favorite set of gaming headphones. They are properly sounding Sennheiser headphones which will sound very good for activities outside of gaming. They are a little more comfortable and have volume control built into the headset which is convenient. The mic is one of the best headset mics and auto mutes when raised. It's a great headset and I wouldn't recommend any other headset. For gaming and calls at work, these are my daily drivers. In every category, these are better headphones, and if you are looking for a budget option to take care of everything and you need a mic, these are the best headphones to buy. The build quality is good enough, but the volume dial on the headset has been giving one of my pairs troubles recently, if I press it against the max I can hear it disconnecting from something but if I leave it at 99% they are still absolutely fine, I wear them every day for multiple hours.
I did spend the time to make an EQ I found listenable with the Astro Mixamp, and I do run the PC37X + Mixamp through my PC and Xbox One much of the time, the virtual surround is nice to have when listening with headphones and does a decent enough job at recreating a real surround system. And having a volume nob for communication audio and game audio is really nice, that is really the only reason I still use the mixamp.
tl;dr: I recommend the PC37X, I own two pairs, they are my favorite headset out there, and compete against pretty decent regular headphones. I don't recommend the Astro A40 headphones, with the mixamp they are pretty good, but only for gaming, and without the mixamp they are low tier. The Astro Mixamp, if you need something to connect to connect to both your TV and PC, and use the communication features of both platforms, it might be worth it, but should only be used for gaming.