You will probably get a lot of opinions and most will be valid to some extent.
I have dived an LX and I own a TX100. I have had both well past 130 fsw in water as cold as 36 degrees F.
If there is any difference between the two, I couldn't tell you what it is.
I believe Aqualung owns Apeks (or at least they did). If memory serves, Aqualung acquired Apeks before they came out with the LX. That may have influenced the design of the LX to some extent.
Honestly guys, both are great breathing machines. If I had to choose between them, I would buy the one I found the most cosmetically pleasing.
I service my own regulators and for me, Apeks service kits are the easiest to obtain. That is the deciding factor in my case.
On a sensitive, calibrated breathing machine under controlled conditions, someone may be able to prove that one is superior to the other. My lungs aren't that sensitive. I have gone a whole dive with my regulator in the 'entry/surf' setting with the cracking pressure cranked all the way up and never noticed.
I have dived some sorry equipment, including a dual hose Healthways reg. Some of that junk would leave my chest hurting by the end of the dive. With the high performance stuff, it is all so good that I don't even notice I'm breathing from a regulator. That is the case with the TX100, LX, anything Atomic, Most ScubaPro, Most Mares, most Oceanic, most Beuchat, etc. Feel free to be offended if I didn't mention your favorite brand or if I slighted your favorite brand.
It's fun to argue about on the internet, but in the end, very few of us could tell what reg was placed in our mouth if we were blindfolded (junk regulators excepted).
There are brands I will not use and would not own, but I keep those opinions to myself. I am very fond of the Mares MR12 first stage and I like metal second stages. Hence, my pony bottle sports a MR12 Voltrex. At depth, in cold water, the Voltrex breathes great. My deepest dive on air was with the Voltrex. Again, I can't tell the difference when using different high performance regulators.
I've never had a good regulator freeze up and I've never over breathed one.
I learned to dive on a dual hose. That should give you some idea of how long I've been doing this.
Bill.