A photo gallery is one of the few kinds of website expected to outlive the software running it. Anyone who kept an archive on Picasa Web Albums, or watched Flickr change its free storage terms, has learned that lesson at least once. Self-hosted photo gallery software puts the images in a folder on your own hosting and the metadata in your own MySQL database, so if a project stops tomorrow the pictures are still files in directories with names you can read.
The hosted alternatives deserve naming, because for a lot of people they are the better buy. SmugMug sells unlimited full-resolution JPEG storage on annual plans, with RAW storage as a paid add-on. Flickr Pro sells unlimited full-resolution uploads with no monthly cap. Pixieset, Zenfolio and Adobe Portfolio all aim at photographers who want client galleries, proofing and print sales without going near a server. Piwigo itself sells a hosted version, Piwigo Cloud, for people who want the software without the hosting.
Open source gallery software wins on three things. The gallery is on your own domain rather than a subdirectory of somebody else's brand, the cost is your hosting plan instead of a per-gigabyte fee that scales with an archive that only ever grows, and nobody can change the terms underneath you. It loses on payment handling, print fulfilment and mobile apps. That is a real trade, not a footnote, and it is worth being honest about before you start uploading.