I work pretty much full-time on SDL Tridion implementations and consultancy. It's a thoroughly impressive WCMS system suitable for large corporations, government bodies, non-profits, etc. For some smaller organisations it might not be a good fit. I have no experience of Fatwire, although I suspect that now they are owned by Oracle, if you don't have Fatwire already, Oracle will be steering you to whichever of their stable of acquired CMSes they currently wish you to buy: this may not be Fatwire.
Indeed - separation of content and layout/templating is a strength of Tridion, as is the separation between content management and content delivery, which allows for highly scalable and secure architectures. For many of their customers these are essential capabilities. Tridion is also well-known for its strengths in international sites, and multi-channel delivery.
As Chopper3 says, you probably need to do some sort of evaluation exercise, or bring in specialists such as Real Story Group or JBoye to do it with you.