- Foundry is hosted via a server or computer. Players connect to it via a simple ip/30000 port link.
- Full script and module support allowing customization
- Refactored code supporting complex layered maps, lighting, and other 'premium' R20 features without the crippling lag associated with them or the price tag.
- You own it outright, 1 time fee 50 or less when it finally releases. Right now it's 5 dollars a month to be a patreon to get access. You can just pay 1 month and get access to whatever version is available and use that forever. Once you have the software you have it there is no version control or being held hostage to a developer. Only 1 user is required to own the software and likewise during beta only 1 user needs to have access to the beta to run games.
- The community mod support is pretty strong. As of right now there are player designed plugins, scripts, and modules to do things like import content from R20 campaigns to ease the transition. Improved NPC/PC sheets compared to the base module support. Improved chat macros and dice mechanics. So on so forth.
In my opinion based on my experience with R20, Maptools, theater of the mind, and a few others I straight up cannot remember the name of... Foundry has been the highest amount of support with the least amount of headaches for VTT platforms. The best part of course being all the current functionality is just 0.3.3 version so it's not full release and more features along with ease of use is planned.
EDIT - http://foundryvtt.com/pages/api.html Might also answer a lot of your GM customization questions.