I generally prefer the neck wallet, so I am not adding bulk around my waist. But, the neck wallet needs to be hid a bit, so I typically will double a scarf around my neck and tie it in the front....one of the really long scarves. I tend to travel with knit tops...turtlenecks in the winter, and long-sleeve light t-shirts in the summer (to provide a bit of protections to my arms). Knits will reveal the boxy neck wallet....especially if you put your passport in it (and I have one of the passports with the extra pages...seemed like a good idea at time, but UGH). Imagine seeing a woman with a big boxy -shaped bulge in front of her breasts.........not attractive and not discrete....LOL. LOVE it when it is jacket weather........hides everything :)
Okay, so what about really hot weather? Then, the scarf can be pretty miserable...even light airy ones. So, then I will often resort to the waist style.....but always with an extra safety-pin just in case.
My spouse (bless his heart) carries the bulk of the stuff in a neck wallet adapted to wear holster style under his shirt, and we then stick cash, passport(s), etc. in a plastic inner bag to keep them from getting totally wet....gross, I know, but that's life (especially in hot weather). We always travel with an extra one, so I can wash and dry the totally gross one and he does not have to put on something slightly wet the next day. In the winter, it is much easier (for both of us).
The negative of the waist wallet for women is accessing it....one has to go somewhere really private to pull the dress up (or unbutton the middle section to unzip and access....not as difficult if wearing a skirt or slacks.
Other than a beach vacation here or there (when we will..the rare times... trust hotel safes), we generally now try to avoid traveling in the heat of summer (for many reasons), so that helps with the neck wallet issue.
My advice....take both for flexibility.
My sister, who is a very good tailor, sews secure pockets into their travel clothing....that works.