@elajenki , another vote for non, from someone who wears both. I wear gortex boots wandering around at home in the winter months, mainly because then I can just walk straight through the puddles and mud. But in the summer most definitely non gortex.
I'm following a guy hiking the TA at the moment, a couple of days ago they had to do 60 plus river crossings in that one day, most of them in the first 3 -4 hours. If they had had Gore-Tex shoes their feet would have been permanently wet, as it was they dried out relatively quickly. Non-gortex shoes are pretty common in the through - hikers community ( PCT, AT etc), although there are always gortex proponents.
If you do a quick search you will find that this question comes up very often here on the forum, there are always a few people that vote for Gore-Tex, the majority however do not. Just like everything it's whatever works for you.