Are there any, real, performance differences between the cheaper ADAT cables and the more expensive ADAT cables?

There may be a few differences in the quality of components, shielding and the joints, but other than that no advantages other than those between a £5 HDMI or USB cable and one of the same length costing £25.
 
Which is to say cheap or expensive, assuming a cable isn't so poorly constructed it results in the digital gubbins continually having to ask for packets to be re-sent, the same bits get delivered in the same way, in the same order and at the same speed. Digital interconnects are not like audio connects, especially guitar leads, where the shielding, capacitance between shield braid and core and whether they make a noise when moved are important.
 

As with anything digital, as long as the ones and zeros get from one end to the other there is no performance difference what so ever between cheap and expensive options.
 
What you should be looking at is the quality of the "cable"  (actually a plastic light guide, NOT an optical fibre) and the quality of the plugs in terms of durability 
 
I have some mid price ones and a couple of cheap ones.  The mid price have "nicer" connectors that fit with a pleasing click, but the cheap ones are more flexible and in my view will last longer because of that.
 
About 25 years ago I bought a reel of about 20 meters of "plastic fibre optic cable" and made my own by drilling a hole in the blanking plugs and glueing my own length of cable.
Can't get much cheaper than that and they worked perfectly.

The reason I asked.... I have never dealt with ADAT connections before. I am now hooking a Focusrite Octapre to a Focusrite Saffire Pro 40 via ADAT. I bought a cheap Hosa ADAT cable. When I crank all the levels up (Admittedly, way louder than I would EVER need to!) there is quite a bit of noise/digital hash in the Octapre.
I don't know if it's possible for ADAT cables to pick up noise/interference or not?
Also, I am getting an occasional, random click noise. I have run DPC Latency Checker and, it shows no issues. So, basically, I am trying to track down the culprit! Ha ha!

They can't pick up noise. A poor connection, however, can result in dropped data which could sound like a random click.

As people have pointed out, digital signals use discrete values which are sufficiently separate, electronically, as to be entirely distinguishable and highly resistant to noise.
 
That's not to say you can just slap down a piece of copper wiring or optical fibre and expect it to work in all digital signalling applications.  For example, the cables used for the 12 gigabit SAS storage enclosure hardware I'm currently working on are highly specialised, remarkably intelligent (they have their own programmable EEPROMs) and have very restrictive specifications which must be adhered to.  When you're signalling at such high rates, the construction of the cable really does matter, regardless of whether it's carrying digital signals or not.
 
So I would say buy a well made cable that's suited to the task it's designed for.  At the very least it should last you a long time if it's well made.  However, do not believe the nonsensical snake-oil B.S. perpetrated by the likes of AudioQuest (those of the *directional* $10,000 Ethernet cable: http://www.theregister.co.uk/2015/02/09/perfect_your_mp3_listening_pleasure_with_this_bonkers_ethernet_cable/)
 
Every time I see the words 'directional' and 'ethernet' together I have to lie down in a dark room for a while...in case there's any doubt, it is complete and utter bollocks.

Ah, Audioquest. Manufacturers of USB cables where:

"SOLID 100% PERFECT-SURFACE SILVER (PSS) CONDUCTORS: Perfect-Surface Technology applied to extreme-purity silver provides unprecedented clarity and dynamic contrast. Solid conductors prevent strand interaction, a major source of cable distortion. Extremely high-purity Perfect-Surface Silver minimizes distortion caused by the grain boundaries that exist within any metal conductor, nearly eliminating harshness and greatly increasing clarity compared to OFHC, OCC, 8N and other coppers.".

Mustn't let those 0’s and 1’s in the USB data packets sound harsh people!

I've a dream of getting a bunch of wealthy "audiophiles" of the far more money than sense type and taking them round a few studios. Where they can see the cables the "pros" use. 100's of feet of thin cables bundled into multicore snakes and Sommer or similar mic leads with hardly a "perfect-surface silver conductor" to be seen and the only concession to "audiophile" standards is maybe using oxygen-free copper to delay the onset of black rot once the cables have been in place a few years.

LOL... I broke up more for the application of those... for your "mp3 collection"!!! What a riot.

I know. What can you say...

Bitflipper: Any idea how I would pinpoint whether dropped data is the culprit?