1/ On technical side, both leaders had very different directions on lots of different details. The main one being: Odoo moved to the web, Tryton was attached to the GTK/rich client.
2/ On the business side (probably the biggest difference): Tryton had a purely community driven development approach (with an anti-commercial mindset of his initial community) and Odoo's goal is to build a great open source product but sustain that with a strong business model (for partners and Odoo Inc).
The Tryton founders were 2 ex-employees of Odoo back in 2008 before the fork. Odoo had 5 employees at that time. (66% of the devs left to work on a fork :)
To discover Odoo:
- Start with these intro videos: https://odoo.com/page/tour
- Test online on: https://odoo.com/start
To try Tryton: http://www.tryton.org/download.html
To try Odoo: https://odoo.com/start
Note that there are also medical apps on Odoo. GNU Health started as an Odoo Projects, some of their leaders moved to Tryton and others continued on Odoo. We deployed Odoo is several hospitals, and 3 of the top 5 medical NGOs worldwide run Odoo.
Disclaimer: I am the founder/CEO of Odoo.