Tenchi Universe is not a sequel to the original Tenchi Muyo anime. It's more or less a reboot of the franchise. It would not be the only reboot they did as they did the same with the Tenchi in Tokyo series.
Universe still has the same concept as the original series though. Tenchi meets some strange women and wacky hijinks happen. Unlike the original series though, the story revovles more around Ayeka this time though. Which is fair because in the original series, Ryoko and Washu tended to have more of the story about them and their enemies. This series also marks the debut of fan-favorite Kiyone to the franchise.
She is Mihoshi's partner in the Galaxy Police, who just can't endure Mihoshi's problems...all she wants to be a top officer in the GXP, but with Mihoshi as her partner, that's near impossible.
The Main characters from the original series return but their stories have been tweaked. For example, in the original series the monster in the shrine was actually Ryoko. In Universe though, the monster is actually Washu. You still get to enjoy the antics of Tenchi, Ryoko, Ayaka, Mihoshi, Grandpa, Sasami, Ryo-Ohki, and the rest of the gang. Though the backstories for all the characters have been altered from the previous series.
The series still has the funny comedy the original had. In a way it's funnier than the original series. Some of the scences in the show are gut-splitting funny. It turns serious in the later half of the show, which the Tenchi series always does well.
It's double the length of the first show, you get 26 episodes as opposed to the 13 episode original series. Though it seems like a bit much, the story and characters never get tired or boring. It's a blast to watch from beginning to end. That's probably the best explanation as to how this series surpasses the original....there is just more of it. Also something else that helps is the fact that it has an ending. The original series ended on somewhat of a cliffhanger, which Universe does not. While the original series got an ending series years later, you don't have to buy 2 series to finish Universe.
The dub is still fantastic and still holds up well to this day. If you want to watch subbed that's fine, though if you watched the show on Toonami it'll be hard to watch without missing the dub.
The other good thing about this re-release is the fact that it is affordable. The Geneon release( which i own BTW)commanded near $200.00 for a USED copy. While it's plummeted with the Funimation release, you can still buy it at around $90.00. That's nice, but the re-release will only cost you about half that.
To me Universe is the best harem anime ever. Only the original series and some of the Tenchi movies are near this level of quality. If you want to see Tenchi at his best check out Universe.
The story is great.
The voicetracks are still amazing.
It's still funny after all these years.
the animation still looks great.
+/- There is less sexual humor compared to the original series.
There is much less nudity than in the original series. Whether you like this or not depends on your point of view.
Cons: Some might not like the way the story jumps from funny to serious.
In the end. If you like Tenchi or want to get into the Tenchi franchise, this is the best anime to start with. Also it doesn't end after the series ends, the movies fall in after Universe. So you can continue the series after you finish Universe. If you come across someone who says there is no good harem anime, show them this series. You won't be disappointed.