This is a really good question. I'll kick off the responses.
First, while a TriCaster running current AE software can simultaneously send an encoded stream to multiple CDNs (content delivery networks), all targets will receive the identical stream. By contrast, MediaDS can send up to four completely different streams. This may involve four unique program sources, or one or more sources encoded with different settings. TriCaster can't do that. So, for example, you might produce different versions of your program using TriCaster AE, but you can only stream one of them; but with MediaDS, you could take the 4 unique NDI outputs from your TriCaster and stream them all at once (Of course, this can involve substantial system resource demands - so migrating those requirements to an outboard standalone system is a big advantage.) And, like TriCaster, each unique stream can go to multiple targets.
While on the matter of program sources - MDS1 supports more source types than any current model TriCaster (and obviously does not require a TriCaster/NewTek pipeline at all). Note, too, that MDS1 can handle up to two streams at 1080p60, which no current TriCaster can do.
There are two other things that make MediaDS a very special device:
The first is the direct integration of Wowza Engine, making it simple to connect video sources to this powerful software. To borrow a sentence from Wowza's website, "Wowza Streaming Engine is the gold standard of customizable media server software for building and delivering professional-grade streaming at any scale." Few would argue with that. Sending the raw RTSP output of the MediaDS streaming encoder to WSE results in 'wrapping' the stream in various ways that make it suitable for playback on all popular platforms.
The second and very important thing worth noting here is that enabling WSE as a destination for one or more MediaDS streams in turn automatically sends its (WSE's) output to MediaDS's integrated webserver, which in turn automatically streams (customizable) webpages complete with a Wowza video player for each enabled stream (the player supports DVR features, btw). Let's consider what this means.
Imagine you are a school, and want to show live video to your students each morning. Think about how complicated it would be to deliver that program as conventional video to every room in the school (or campus, or office building, or hospital, hotel, what have you). With Media DS, all you need to do is plunk the unit down somewhere, plug in power, kb mouse and monitor, connect a video source (a webcam would do as a minimalist approach) and connect it to you local network. Now everyone with access to that network can hit a URL you provide on pretty much any device with a web browser and watch your live stream - no CDN or even Internet connection required. This one little box handles everything you need to be your own CDN other than a camera. And of course, if you want to take advantage of WSE's more advanced capabilities (for the purpose of international scalability, etc.) you can do that too.
Well, maybe that's a good enough start.