The ending of Underworld: Rise of the Lycans shows Lucian seemingly destroying Viktor, who is in fact left in hibernation, and that is how the prequel hands the story to Underworld (2003). Spoilers follow, and the second half is my opinion.
After Sonja's death at Viktor's hands, the war between Lucian's Lycans and Viktor's vampires breaks into the open. Lucian storms the fortress and appears to kill the elder, but Viktor is only sealed away in a long sleep. The closing scenes then lead into the opening of the 2003 film, with Kraven's voice and a brief glimpse of Selene. That is the bridge: the Death Dealers keep hunting Lycans, and the war Lucian began is still running when Selene starts to wonder why the Lycans are following Michael Corvin.
Why does Viktor survive? Bill Nighy plays him in Underworld (2003), so a clean kill was never available. In my opinion, that is the prequel's biggest structural handicap, because anyone who has seen the first film knows the duel's outcome before it starts. Paradoxically, it also explains the film's shape. With the result fixed, the drama has to live in Sonja and Lucian, and in the cost of the revolt, since the cost is the only thing the audience cannot predict.
How does it compare with the rest of the saga? Underworld: Evolution (2006), directed by Len Wiseman, runs 106 minutes and picks up Selene and Michael's story. Rise of the Lycans ran 92 minutes on a $35 million budget and made more than $92 million worldwide, according to Box Office Mojo. That is a smaller canvas, and it suits a tragedy about two people in a fortress better than it would suit a chase film. Underworld: Awakening (2012), at 88 minutes, is shorter still but spends its time on a different Selene entirely.
There is a production angle too. Patrick Tatopoulos, who had designed the creatures for all three films, directed here for the first time, according to Screen Daily. In my view that shows in the finale: the Lycan army is the point of the climax, and the creature work carries the storming of the fortress where a first time director might otherwise have leaned on dialogue. Wiseman moved to producer, so the look of the earlier films stayed in the family.
If you have just watched the prequel, the natural next stop is underworld 2003, where Selene's investigation begins.