Shinpi no Sekai El-Hazard

The same person designed both serieses. While El Hazard is not strictly a Harem anime like Tenchi is, there are still a lot of similarities between the two. 

both main character's friends are hyperactive busy bodies explosions powers skimpy outfits new worlds 

Pretty similar in how the world feels like and the character constellation. Strange new world with harem/romance undertones 

Both works are produced by Pioneer LDC, and many girl characters appear. 

Same creator. Similar perversions. Similar comedy types though photon's are closer together. 

Not so much similar to this anime as it is to the video game it's based on, since it barely even acknowledges the world it's set in. That said, both of them use the motif of a collapsed technological civilization that people have built around without really understanding. El Hazard is a very tongue-in-cheek telling of the standard "people from our world find themselves trapped in a magical new world", but manages to do it in a way that's still resonant. The characters are charming and have a good chemistry with each other. While the story gets bogged down by some directionless world-building and much of the comedy falls flat, it pulls itself together in the last episode for a poignant, haunting ending. read more 

Both anime series spirit the main protagonist in a fantasy world and both characters receive magical powers. 

Both series involve a group of friends and classmates are transported to another world.IN both series the male lead's rival sides with the bad guys while the male lead and everyone else sides with the good guys. 

Dual has the same underlying storyline of a displaced main characters that ends up in an alien environment. What makes Dual so interesting is that the cast ends up in a parallel universe where all the character's counterparts have slightly different personalities than what they had on Earth. This spawns a great deal of situational comedy while cleverly interweaving romance into the story. 

Both anime are from the '90s, even the same year. They are fantasy with magic and slapstick comedy and have clever dialog and optimistic heroes. Sometimes they seem to break the third wall.