There is a web client. You can test it at http://health.gnusolidario.org:8000/ with database: health30 Username: admin and password: gnusolidario
About the desktop client, ugly is a matter of taste but at least it is very efficient for intensive usage (like daily encoding)
To be more precise about Tryton differences, it has both a desktop and a web client.
About the "anti-commercial mindset", indeed it is that the Tryton community does not allow lock-in mechanism into the project (at the opposite of Odoo with the business model of paying updates to new versions). But also it does not place a commercial entity as the center of the project but instead a non-profit Foundation.
"Odoo's goal is to build a great open source product", this is also the goal of Tryton project but everyone is free to choose its business model.
It is not really fully Open Source. Since they changed the license [1], they adopted a open core model and so most of the new features (UI, reports, etc) are only available as private software.
Also they have a quite strange interpretation of the xGPL license mixed with proprietary license.
Users of their SAAS service should be careful to not install those private software otherwise they will not be able to change of hosting service.
