Tenchi Universe is based on the same characters but adds Kiyone to the story as a balance to Mihoshi's ditzness. The story starts out differently also. Instead of being a demon, Ryoko is only a space pirate that crash landed on Earth while being chased by Ayeka and her sister Sasami. Mihoshi was also involved with trying to arrest Ryoko. Instead of being Kagato's prisoner, Washu lands on Earth in a stasis pod where she had been trapped for 700 years. Kiyone comes later after being sent to Earth to retrive Mihoshi and the Princesses.
Tenchi in Tokyo
Tenchi in Tokyo uses the same characters as Tenchi Universe. Although the story about how they met changes yet again. Now Ayeka, Sasami, Mihoshi and Kiyone are chasing the space pirates Ryoko and Washu. Ryoko and Washu stole a Jurai crystal filled with Jurai energy. Ryoko had to land their ship on Earth in search of power strong enough to refuel their ship. Washu located a power nearby and surprise, it's centered around Tenchi. Ayeka and Sasami land on Earth to hunt down Ryoko, so Mihoshi and Kiyone do the same.
Tenchi Muyo is an excellent additional to the harem anime shows. Unlike Oh My Goddess, the girls are less submissive and more believable as they all have their own agendas. The dvd is basic with no real improvement over VHS quality, there are a few extra scenes that were cut or censored in the Cartoon Network version, but overall Tenchi Muyo is a good feel good innocent[ish] anime.