I have both php apps running on my hosted platform. I don't have a :"virtual server" it's just a PHP and MySQL hosting service, so I can't host anything which requires more than this.
Gallery3 advantages
It's much smaller. Ignoring the photos (and thumbs, resizes etc.), my G3 install is 22MB whereas Piwigo (with the Bootstrap theme) is 190MB. That's a huge difference.
It's easier to customise - Piwigo has so many templates and defaults and over-rides that the same style could be defined in more than five places, and trial and error is needed to work out where to make the change, only to discover that the recommended way (in a local config file) breaks every other theme you may want to use in future.
The photos are uploaded to a nice directory structure which mimics your album hierarchy.
I have a module (iptcedit) which writes photo title, description, captured date, GPS info (latitude, longitude, altitude) to the photo. Many of my old photos had no EXIF/IPTC info so I entered it into G3 directly. Now, they're written to the photos so I can easily migrate if necessary.
I have a nostalgic attachment to G3.
Piwigo advantages
It's still current. It's being developed, although it's almost as "old fashioned" as G3 and many modules/forum posts are 10 years old.
It's fast. Noticeable faster than G3, although I'm not sure why. I need to investigate.
It's customisable once you get to grips with tpl, css, scss and more files.
It has more users and hence a more active support forum. Just.
Summary
I don't mind Piwigo. I've done some minor customisations and got it looking ok.
I still prefer G3 but that's mainly because I'm used to it. I like the fact I can write out IPTC tags, and I really like the fact I can upload photos in the app itself. With Piwigo, if I use the in-build upload feature the photos aren't organised on disk, but are in "virtual" albums within Piwigo. I have to FTP them to the server and do a "sync" if I want a proper hierarchy.
G3 is much smaller in size, hence much easier to find out what to edit when I want to make customisations. It runs under PHP 8.3 so has life left in it.
Piwigo is faster. I'm not sure why, as it's so large, but I assume it uses more modern libraries (or whatever).
I feel like G3 is "mine" (as I know it so well after many, many years) whereas Piwigo doesn't feel like that.
I'm sticking with G3, but if I had a website open to the public I'd probably go Piwigo for the speed and support.