There are a lot of variables here so you won't get a hard-and-fast response.
It will depend on the stiffness and construction of the boot, your usage, the amount that you sweat, the terrain and the weather.
Those who dislike Gore-Tex boots find that:
- Under heavy use the membrane degrades and fails, often within weeks.
- Breathability is compromised and sweat builds up inside the boot. Your feet can sweat over half a pint (280ml) per day so for many this is a significant issue
- If the boot gets wet it takes significantly longer to dry.
In threads like this where experienced walkers gather, the general view is negative, though some users do find it works for them.
The downsides seem to apply with particular force to lightweight boots and shoes - I've met many people on the trail who were less than delighted with their lightweight GT footwear. But if you are using conventional leather boots, it's harder to see what Gore-Tex offers compared to traditional waterproof dressings.
My only personal experience was picking up a pair or GT trail shoes in a sale and they seemed to give the worst of all worlds - after the first few hours they let water in but didn't let it drain out. But then I walk off-trail on Dartmoor, which is as bad as it gets underfoot, so your experience may vary.
I would say that in general it's casual users who seem to like GT boots, while walkers who push their equipment are less enthused. In tough environments like Dartmoor and Scotland I've certainly met far more critics than fans.
For any particular boot you may be able to glean something from the reviews. If you can afford to take a punt, try it and see if it works for you. If funds are tight you might be safer buying something more traditional - that way you know what you're getting.