Mini-ITX system for travel, advice?

Lian is the best case of the two. When comparing an all aluminium case to a steel plastic case, you're going to be much better off with aluminium. The Lian Li will run much cooler as the Aluminium is much better at absorbing ambient heat from your components and much much lighter compared to a hot/heavy steel and plastic case.

Also, the Core i5 3570k is going to be your processor of choice. Benchmarked together, it is just much better and faster for all things and can be overclocked relatively easy.

Both of the cases you picked out are probably among the best available when it comes to small size.
What is important is how you actually travel. If you want to carry it lose, then the Lian Li, with the handle and reinforced corners, is likely to be more durable than most. If you pack it in a suitcase or whatever, then this becomes far less useful, and you really want something which is suitcase friendly. This might be something squat but deep, like a Coolermaster Elite 130, or slim and flat like a Silverstone Raven RVZ01.
As a side note of limited help to you, I recently transported the much-maligned Bitfenix (Prodigy) Fatboy in a suitcase, and while it more or less filled it, I didn't have any issues at all, so you might be surprised at how much potential flexibility you have.

Also, I'm going to throw out a slightly counter-intuitive idea. I'm the first person to say "Don't try and do high end AMD builds at anything other than ATX", but if you already have a stock-clocked 8350, and haven't overclocked/have no intention to, then there is a possibility of converting your current system into something more travel-friendly. 760G boards are basically outdated, but they do come in mATX form, and there are a lot of mATX cases which may suit your needs (though they won't touch things like the Hadron for size). A compact mATX tower like an Arc Mini is a something to consider, as it really is very conventional, but there's also more unusual forms like the Silverstone SG09/10 which is very boxy but in terms of volume, pretty tiny. It's worth considering at least.

As for 760K versus 3570K (though that should probably be 4670K/4690K), there is quite a world of difference. The 760K is a great budget-friendly CPU, but it really can't compete with i5s in any tasks really. Something to point out though - Intel do make other CPUs. A stock clocked 4430/4440/4460 is in many ways far better price/performance than the K-series CPUs, at around ~£120+. This also has an advantage in that it doesn't need to be paired with a Z-series motherboard, though the savings here can be minimal if you need a Wifi integrated motherboard.

No problems, smaller PCs fascinate me.

I'd still go for an i5 if you can stretch that far. At the low end a 750K/760K is a great little CPU, but when paired up with the likes of a GTX770 you're likely to be a little CPU limited in some games.
If you look at 4000-series i5s as a range, they are effectively all the same CPU running at different clock speeds (there are a few minor differences to things like the turbo function, but these aren't hugely significant). The K is simply for the overclockable models, so the best value i5 is almost always going to be the cheapest one on offer. As I mentioned before, I'd look at the 4430/4440/4460 which run at 3.0, 3.1 and 3.2 Ghz respectively.

To my knowledge there isn't an easy way of comparing PSU depths (it's something that comes up fairly often on smaller builds). Off the top of my head, the Corsair CS range are 140mm long. They wouldn't be a normal recommend for me, but they should be reasonably solid and fairly easy to get hold of.
Few others - Antec EA 550/650 Platinum, Silverstone Strider Essential Gold 500/600, Silverstone Strider Gold 550. All of those (other than the Corsair) are made by FSP, who also sell some under their own branding which have the same 140mm depth.

I wouldn't say there is a good or bad motherboard company to go with. Asus, Gigabyte, MSI and ASRock are the big four, but due to the form factor there isn't a huge selection anyway. If you want bang/buck, then going for a super cheap H81 ITX board like an Asus H81I-PLUS is great value, but if you need Wifi then the price basically doubles when you are looking at the likes of MSI H97I AC and Gigabyte GA-H97N-WIFI.

I probably wouldn't bother with the cooler or a 650W PSU if you can get a 500/550W version for cheaper, as you really don't need the headroom, but otherwise it looks fine.
For the cooler, the Intel stock cooler should suffice, and if you are going to spend a not insignificant amount on a cooler like that, it's worth bearing in mind that Noctua don't recommend it for these CPUs.


For the motherboard, make sure you don't need any additional features as H81 boards are fairly sparse but some of their limitations are lessened at ITX form due to size limitations.


Also, incase anyone else mentions it, pcpartpicker does have a compatibility checker for CPUcoolers and PSUs, but I have found it incredibly unreliable.

SATA 3 = 6Gbit/s
SATA 2 = 3Gbit/s

Understandably confusing, you'll see a lot of people mention SATA 6, which technically doesn't exist yet.