There are definitely advantages to companies. As an end-user, the only advantages I can think of are data centralization and device portability.
While we're talking about "webapps", generally, and not SaaS specifically... the two often go so hand in hand that it is the exception to see a webapp that is not also a SaaS product.. and as a consumer I kind of mostly hate SaaS.
With the above two advantages noted, lets look at the cons:
- Companies can, and routinely do, push unwanted UX changes on me without my opt-in. Pre-SaaS you would wait for a new version to come out and could see what the reviews were saying before deciding if you like the changes and want the new features. Now you're a guinea pig and get the new "features" whether they are a benefit to you or not.
- Forces me to have my data on someone else's computer
- The "other peoples' computer" issue means that if there is a software or a hardware failure that prevents me from being able to do urgent work that it is entirely outside of my hands and my ability to troubleshoot the majority of the time (though this is a double edged sword since for the average non-technical user it can be a big benefit)
- Can't work without an active Internet connection (though I'll concede that not having an active connection is becoming pretty rare these days)
- If the company goes out of business, say goodbye to your data in the majority of cases
- Often goes hand in hand with renting the software rather than paying a flat fee for a perpetual license. Given the choice, I will always opt for a perpetual license. I try hard to have as few recurring payments in my budget as possible. Utility bills are bad enough.
If, however, by "webapp" we just mean a desktop application that uses a DOM-based rendering engine then I couldn't care less. There are tradeoffs, but they are purely technical and rarely impact UX directly in the way that a general approach to software delivery and consumption does.