SDL Tridion is used to manage multi-lingual content for a large product website. It is implemented in the entire organization and local country business units use it to update and maintain content in several languages. It allows separate maintenance of content and layout, and is excellent at sharing the content to all country language websites.
SDL has a better API and also handles high server load much better. Also, the built-in integrations for translations are more suited for performing lots of translations for many sites. However, Umbraco, like Tridion, has a great community and finding solutions with both platforms is very easy.
Well suited for large international organizations where they can use integrated and automated translations with SDL's language translation tools (World Server, Translation Management Server). With the newer SDL Mobile and SmartTarget modules it is possible to offer more customized and dynamic experiences. However, the strength is definitely in the product architecture and well thought and documented APIs. It handles high server load easily due to this architecture. Managing large multi-lingual websites also is good and fast to rollout additional language websites by reusing existing translations. However, if you have a small website with 1 Content Editor then there are lighter systems out there for those needs.
SDL Tridion is used by many of the largest brands in the world and SDL continues to refine their product. The great backwards compatibility in the API and continued support of the community reinforces the ability to provide successful support of the platform.
The editor user interface is very user friendly and in-site editing makes simple updates fast and easy. The extensibility of Tridion is a big plus and the ability to add our own options into the default Tridion interface helps us integrate with external systems. Finally, the user permissions and security system helps us deploy it within our large organization.