They will service your watch (details on the website) or take it to any good watch place and they will do it for you as well. CW have been around for years now and are doing very well. They're not going anywhere and their watches are excellent. I'm not saying they're as good as Omega or any other high-end Swiss brand, but they're very good and people shouldn't hesitate if that is the particular brand they're after.
They have only been around since 2005. Thats not much of a track record to know how long they maintain an inventory on parts or what their policy is on that. Eterna has been around for decades and parts have not always been easy to obtain for their watches. Yes, since the CW uses an ETA movement, almost anyone can work on it. However, if you damage a bezel which is specific to their watch, whether or not you will be able to obtain one in 10 years is anyone's guess. Companies like Rolex (and probably Omega, IWC, Breitling etc.) guarantee a stock of parts for their watches for at least 20 years after production ends.
The original poster asked in reference to the CW "I'm wondering if the difference in quality is worth the difference in price or if I should keep saving up for the Omega." IMHO, you get what you pay for. There is a reason the CW is less expensive than an Omega. Whether or not someone wants to spend the extra money for an Omega is something only they can decide.