TL;DR - I'd cautiously recommend the refurb Asus w/ Intel. For most cases, the difference between a 2.5GHz Ivy and 2.6GHz Haswell should be marginal, and it comes with a slightly faster GPU (both based on Fermi), and is a fair bit cheaper. Further reasoning below...
So with Intel's naming scheme, which is pretty messed up and not really comparable to the desktop naming, as there are a lot of Mobile Core i5's that have way more in common with the desktop Core i3's vs Core i5's, I think the only difference between Core i3 and Core i5 in mobile is cache size and Turbo Boost. Anyway, the first digit is generation (2= Sandy Bridge, 3= Ivy Bridge, 4 = Haswell). The second digit is the performance class, and third further differentiates performance within the class, and the last digit as well as suffix seems to indicate misc things. Off the top of my head U= low power BGA (soldered), M is socketed, standard power, and Q indicates quad-core. I have the Core i7 4810 MQ, so that means it's Haswell, very high performance (really amongst the fastest mobile Intel CPUs), slightly faster than a standard 4800MQ (100MHz faster in base and turbo clocks), socketed, so I can swap it, if I so desired, and it's a native quad-core.
So, as for 4200m vs 4200u, the U will provide better battery life and lower heat output by sacificing performance. If you don't care much about portability and batter life (which I'm assuming you don't since you're considering a 17"), then the 4200M, hands down. Now compared to the Ivy Bridge Core i5, the haswell should be only slightly faster in most applications. The biggest updates that Haswell brings are updated graphics (not necessary if you're going dedicated), lower power consumption (again, not important as a gaming part), and more advanced instruction sets, which can provide a noticeably improvement (20-30% I believe, possibly more), but the applications that use those instruction sets are few and far between, and will likely not work it's way into gaming. IMO, the differences between the 4200M and 3230M aren't big enough to be a deciding factor.
NVidia has the worst possible naming scheme ever. Both the GT 635M and 820M are Fermi based, meaning they are essientially re-badged 500 series GPUs, but which is hard to tell because the 635 has several variations resulting varying in clock speeds, core count, and memory bus bandiwdth, as well memory types. However, I think in either event, the 635 will be at least slightly faster than the 820.
Now, with regards to the R7 M265, it's the fastest of the bunch, but not by too much, but the CPU it's paired with isn't suitable for gaming, but it can play a few games. However, it would make for a good student gamer (if you're the kind that likes to game at coffee shops, or in between classes), as the GPU has Zero-Core (completely shuts off when not in use) so it has the potential to get some pretty good battery life as well.
The last system you brought up appears to be a good deal, except their are some QA issues, especially in regards to the screen, from what I can tell by the reviews. Also, storage, which is the main bottleneck in modern computing, and it isn't easily upgradable on that computer (requires removal of keyboard and ribbon connector), so, for me personally, I wouldn't touch it with a 10ft pole, especially with Newegg's return policy (took me almost a month to replace a stick of RAM, and that's with their Premier service).
With that said, if form factor is no issue, then I'd cautiously go with the refurb Intel powered Asus. I'd imagine on most laptops, the main issues would be HDD failure, but that's an easy fix (usually).
- Compal KHLB2 - replaced stock drive w/ 640GB 7200RPM, which I then replaced with Corsair Force F60A SSD
- Acer AO722 - replaced 320GB 5400RPM with 64GB Crucial M4 SSD
- Clevo W240SS - bought as barebone and installed a 240GB Crucial M500 mSATA, along with a 1TB Toshiba SSHD (8GB NAND cache)
- see a pattern?
On all these laptops, performance was dramatically better in everyday tasks. I only had a performance issue with the Acer, since the AMD C60 (1GHz dual-core Bobcat, which is a low-power architecture) it came with was a bit too anemic for much of anything. I was beginning to think I wasted money on the SSD, since it was too slow. It wasn't until I re-intalled the stock hard drive almost two years later that I realized how much worse it's already fairly poor performance was. Something as simple as system updates took dramatically longer. You could blame Windows Update, because that takes long in general, but even on Linux, it took at least twice as long to update. I never doubted SSD performance again, even with severely anemic CPU's with only single-channel memory. That experience actually influenced my decision to get a SSHD has a storage drive vs a purely mechanical drive on my newest laptop.