One problem that Stargate had was the advance in tech through the series. It lost its core aspect of a hopelessly outnumbered and outgunned crew going up against the universe and winning.
That's not a bad thing, after all the winning was the point, and the constant movement of technology and growth of characters, while maintaining an episodic format, was good.
However it meant in the end the show was stretching credibility with it's plot (a secret military organisation with tens of thousands of people in the know, multiple space ships flying around the place, alien attacks, multiple governments, and it's still secret?), and continuing from that point, at least on Earth, would be a very different show. By the end of season 8, they'd conquered the galaxy. There wasn't need for ingenious solutions like blowing up a sun any more.
Trek however hasn't really had that, the technology used by the end of DS9 or "Renaissance Man" was pretty much the same used at the start of TNG. New technologies introduced (transwarp beaming, phase cloaks, slipstream, Warp 10) didn't stick for a variety of reasons, and it was made clear on many occasions that the doctor's emitter could not be reproduced. There was still a whole galaxy unexplored to use as a canvas for telling the stories.
However as time goes on you have a lot of canon to follow - and a lot of people who won't like inconsistencies, this can be detrimental on story telling. Continuing 80 years after the end of DS9, with Captin Bango and the voyages of the Enterprise H could work, they could ignore older trek most of the time just as TNG did, and allow the novels to fill in the "Lost Era" time. No reason why you wouldn't still have warp drive fast enough to get to the plot on time, but slow enough to make it nail biting, quantum torpedoes, phasers, etc. It would still be difficult though, TNG had 4 films and 79 episodes before it. A new series would have 10 films and 700 episodes behind it.
I suspect the new series will be like TNG, but set in a different universe, with no canon other than events they choose to take. They'll have the fact that Zefram Cochrane broke the warp barrier, but it wouldn't be in 2063, it wouldn't be with Riker + Geordi on board, Khan wouldn't have been taking over the world in the late 90s and then getting frozen, but there may have been genetic badness happening in the 2100s. When they go back to 2024 in a season 7 episode the Bell Riots won't be erupting, but in 2084 there may be some form of civil unrest.