Corsair 400C vs NZXT S340 - CPU cooler size

I'm thinking to get new case for my gaming PC. I found Corsair 400C and NZXT S340 but I have Cryorig R1 Universal cooler and I have no idea if I can install it in these cases.
CR R1 has 168mm height.
NZXT has info about maximum size of 161mm CPU cooler but if it's true or there is still some space ?
Corsair is not saying how big air cooler can be installed. They clearly promote their AIO. I saw photos with Noctua NH-14 but it's 161mm cooler and I can't see if there is 1mm or 20mm left.

I'm not decided if inside will be air or water cooling and I'm changing motherboards from time to time but I want it to support CR R1.
Actually I wanted micro ATX case but I see that something like Corsair 350D is barely smaller than full ATX. I also can't find any better option for my needs that also look good. I wish white case what is also a problem looking at available models and my personal preferences.

I'm not decided if I put there 5820K+micro atx board or 6700K+full atx. No real difference as one of these setups is collecting dust and I don't want to sell it as I need both for tests.

If you have any ideas what other cases are good or know how big air cooler can fit into mentioned cases then please let me know.

I ordered Corsair 400C as it has some more space for cooling and found it with free shipping and $10 lower price.

Straight in the tech specs on the Corsair website for the 400C it lists 170mm CPU cooler height.

I noticed max cooler height yesterday and that's why I decided to order 400C. I don't know how I missed it earler.
I will probably use water anyway but I'm not sure so I'd rather have some more space. I already checked couple of cases and nothing is perfect for me. I actually wanted white case but there is nothing that I like and Phanteks is or way too pricy or badly designed for my needs and too big. These white are black inside anyway.
400C has some more space for cooling inside than S340 and somehow I'm more convinced to Corsair than NZXT. We will see.
I started to look for micro ATX case but everything good is almost as big as middle towers which are supporting full ATX mobos. At the same time micro ATX cost more. Weird market .. I have ~2000 cases in online store but at the end I find 3-4 max which are interesting for me.

I see that many manufacturers are designing their cases to work with AIO. There is info about full support for water cooling but who will keep CPU and high performance graphics card on single 240mm rad. On nearly all photos are installed AIO for CPU, pre-installed 3-5 fans and there is info about silence ... how can it be silent with high series graphics, couple of fans and buzzing pump in AIO ( barely any pump is silent ).
On the other hand who wants to have full tower case for micro atx motherboard, single graphics and one SSD...