I've been working on deploying Odoo for a small manufacturing company.  For many reasons we run Odoo locally on our own servers. Getting our deployment up and running has been challenging. 

The software in and of its self is robust and stable, however, to really dial in and configure to your local needs, you will need to be comfortable creating and editing both python and xml files. 

For example, when you are running a local instance, it will kindly alert all users that "Your Odoo is not supported" at the top of the web page.  It is an important reminder, however, if your job is supporting that local install of Odoo, you will want to turn it off.  To do so requires downloading a module and installing it. (see http://superuser.com/questions/808850/how-to-remove-your-odoo-is-not-supported-upgrade-now-or-register-your-contract for more details.)

Without a doubt I'm sure an easier way to accomplish this could of been built in, however, if you don't posses the skill to accomplish this moderate task, perhaps your data would be safer with the SaaS. 

I've found that Odoo is kind of like a car.  Well built and more than capable, it requires some training and experience to really get the most out of it.  You can get hands dirty and change your own oil, or you may find it easier to take it to the shop. 

I did review the trial of the SaaS to see if it was in some-ways more functional.  In particular, I was looking for a functional configuration of the payroll system for the US.  As is, both the SaaS and the local deployment to not really have a fully functional payroll system if your business is located in the US.  You will need to understand the development side of Odoo to modify it store the additional data needed (deductions, tax tables, emergancy contact info to name a few) and build the additional interface structure.  So far we've found it more cost effective use a payroll service to make sure our taxes are right. There was no hidden solution that I could find in the SaaS and I suspect real benefit of the SaaS is the access to trained people to help you over these types of hurdles. 

A major thing to be aware of is when it comes to major version changes.  If your running your deployment locally, you are on your own.  If you are using the SaaS, they will help you migrate your data between major versions.  However, I think that you really understand how to configure and use Odoo, this should not be that big of a challenge.  (see https://www.odoo.com/forum/help-1/question/upgrade-to-openerp-odoo-8-52844 for more details.)

Best of luck in your deployment and let us know how it goes. Remember you can install the Demo DB to examine a functional euro-centric deployment. 

P.S.  You should probably read this.  https://www.odoo.com/documentation/8.0/howtos/backend.html