How do industry funded theses differ from purely academic ones?
Your thesis must satisfy the requirements of your committee and university. In that sense the thesis coming out of an industry-sponsored project is no different than a thesis coming out of a government research grant. How you get there, and what happens along the way may differ compared to your peers.
Some differences to consider while working on an industry-sponsored project include:

(1) Additional oversight by your industry contact/group. They are sponsoring the research for some reason, and would like to keep it on track toward their goal. Often this includes meetings and reviews on-site at the company (see #3 below).

(2) Potential delays in publishing or releasing data to give their patent process time to run. Of course, more universities are looking at building a patent portfolio as well these days, but be sure to clear your conference and journal submissions with your industry contact. Up front find out how long this usually takes and factor it in to your submissions.

(3) Remember that you are auditioning for the company, particularly when visiting them. If you do well you might well get a job offer out of it (this is a prime reason for companies to sponsor research at a university by the way - a talent pipeline). 

(4) It is entirely possible that you will be encouraged/asked to attend one or more industry meetings. While not as 'prestigious' as an academic conference, it would give you exposure to lots of companies that might want to hire you. 

(5) You get to work on a problem that somebody else cares about. Taking something from research to development to product can be an exciting thing to do, and is not commonly a feature of university-based research projects. Either liking or hating the experience you have with the interaction can be a strong indicator of what you really want to do after your PhD.