I have traveled with the Berky "travel" one. It is not for travel, not at all, other than it is smaller.
I put it in a 5 gallon bucket next to foam rubber and bungee the bucket still.
The shaking and vibration surly seem that it would tend to unscrew the filters. I use Flurde filter and it has to be screwed in exactly, no more, no less, turns exactly, so if those move then it does not work.
That said, I have had no problems with it traveling other than it is cumbersome and takes up space given the bucket situation.
A better solution, more expensive, but much more useful and travel-worthy is
Lifesaver jerrycan.
It is robust, and can be pressurized so the water squirts out and can be used for a shower even. It travels better than a counter top dispenser.
I don't think I will trust Zerowater's assessment of their competition's performance. I do not doubt that they had bad things to say about everyone except their little dinky pitcher filter that probably only makes the water taste better. Look for more quality filters if you want clean water. Berky is a good reputable brand, but not the only one, Pur??? LOL, just lol.