Just as with Mayuka in Manatsu No Eve, Ryoko's suspicion of Sakuya is born out of her own love for Tenchi/jealousy for his affections but with perhaps a touch of something else as well. From pretty much their first encounter, Ryoko refers to Sakuya in derogatory terms - as a sneaky witch, a schemer, someone plotting to steal Tenchi away...all very negative, conspiracy suggesting words. In Manatsu No Eve, Ryoko detects the dark spirit at work behind Mayuka's behaviour. However, there's no such connection given to us with Sakuya until very near the end. It just seems to be Ryoko's intuition - or of course, plain jealousy. What has to be understood, is that Tenchi in Tokyo is written on the foundation that Sakuya is Ryoko's competition for Tenchi. Not Ayeka. (Nobody bothered to tell Ayeka this, I hasten to add...but anyone looking at this series has to see that it's the basic truth! Even the artwork on the DVD menus shows Sakuya and Ryoko back to back...no sign of Ayeka at all.)
Ryoko's dislike for Sakuya exists on many levels. When she thinks Sakuya has stolen the gems that mark their bond with Tenchi, she threatens her with physical violence (and in a sense she is not far wrong, since although it isn't Sakuya who has taken the stones, it is connected to her through Yugi and her manipulation).
Yet, when Ryoko sees Tenchi kiss Sakuya, she does not resort to violence against the other girl. Instead she seems defeated - angry and bitter but unable to confront Sakuya face on about what she's seen. She takes off to space with Hotsuma rather than try and face either Tenchi or Sakuya again...only returning when she realises that what she had on Earth meant more to her than the pain caused by that kiss.
Sakuya's first impressions of Ryoko are of awe and wonder as she watches her take on and more or less defeat Hotsuma to rescue both Tenchi and Sakuya from the House of the Eternal Pledge. She never discovers that Ryoko is an alien - more, she believes she's some kind of sorceress, and apparently that seems normal enough to her. But then again, Sakuya is just someone else's shadow...so I suppose we shouldn't judge!
Sakuya is the one who points out to Tenchi that he has feelings for Ryoko - or as she puts it, "someone else waiting for him" - after she's stalked him to the park when he's on his date with the pirate. That she sees all of Tenchi's 'housemates' as a threat is clear, but of all of them I suspect she sees Ryoko as the biggest - both in terms of physical violence and emotionally, too. Unfortunately, direct rivalry between Sakuya and Ryoko on a relationship level is pretty much avoided by Ryoko's leaving of the Earth to join Hotsuma...but then, Tenchi and Sakuya become closer WHEN Ryoko has left the earth, which indirectly does suggest she was a force keeping them apart. Okay, maybe that's speculation. But still, Sakuya never does completely erase Ryoko from Tenchi's head, since he has two flashes of her when she is in trouble while he is supposedly out with Sakuya. Their rivalry is more virtual than actual in some ways - but it still reminds me again here of the rivalry with Mayuka in Manatsu no Eve or with Haruna in Tenchi Forever. Flashes of Ryoko distract Tenchi while he's dating Sakuya. Flashes of Ryoko distract Tenchi while he's living with Haruna. Ryoko's presence breaks Mayuka's spell over him. Just common sense, really! Ryoko and Sakuya are just another battle of reality versus fantasy in the Tenchi-verse!