climbing shoes
I don't have any lace climbing shoes, but so far I know quite a few people who have Velcro shoes that have torn and the Velcro strap is no longer attached. My shoes are actually very close to tearing it seems as well.
I have never seen anyone whose lace shoes have torn though, but I'm sure it happens, I just don't know at what rate compared to Velcro shoes.
There may be some brands that have similar sizing, most likely by chance, but overall brands can have very different sizing to their shoes. Even different shoes from the same brand tend to have different sizing.
I believe he said in one of his recent videos, or just in a video he was in, that he downsizes his shoes a few sizes less than he used to a few years ago. I can't remember the reason why he said he does it.
I would say you should always try them on and see what works for you. The same principles apply to choosing neutral climbing shoes as they do to choosing aggressive climbing shoes - try them on and feel what feels best for you.
I would keep in mind the intended usage of the shoes though, since if you are getting neutral shoes, you may be climbing longer routes such as in sport and trad climbing, in which case, downsizing to something very tight may feel very painful and uncomfortable due to wearing the shoes for so long.
For me the fit of climbing shoes has always been the same based on the shoes. I haven't changed my shoe size since I started climbing a few years ago, even when I try on shoes I already have, like the Evolv Shaman 2, I still find that the best fit is the same size I got when I first bought them a few years ago.