John Cena would have still ended up the top dog. He had (and still has) more natural charisma, mic skills, merch sells and is generally more relateable to the audience than Lesnar ever was. Batista's breakout in early 2005 was a hotter period for him than Lesnar ever had during his initial WWE run, and yet they still had he and Cena switch places on Raw and Smackdown (by moving Cena to the A-Show and Batista to the B-show.) Don't think that Lesnar being there would have prevented Cena's rise to main event level. In fact, I think it was speculated/rumored/confirmed that the original long term plan was for Orton to beat HHH for the WHC and for Cena to defeat Lesnar for the WWE Title both at WM21. Well, Orton flopped and they went with Batista instead, and JBL ended up dropping the title to Cena instead of Lesnar... which highlights one thing that WOULD have definitely been different, and that's JBL. He was pushed as the top heel of Smackdown primarily BECAUSE Lesnar left, leaving them without a top heel (and Angle was injured, so leaving them really without any main event level heel at all.) If Lesnar never leaves, the JBL gimmick ever existing is called into question, and he certainly never gets an almost year long WWE Title run.
Assuming Lesnar stayed, he would have feuded with Cena a few times, we would have gotten Lesnar/HHH much earlier than we did, Lesnar would have gotten a streak match with Taker at Mania at some point (and probably a few other PPV matches with him as well), we would have already gotten Lesnar/Batista, Edge would have still broken out as a superstar and as a babyface would have likely feuded with Lesnar at some point, etc. So yeah, there'd definitely be a shakeup and I don't see Cena/Orton/Edge having as many ridiculous amounts of title reigns as they did, but I don't see it being much different as to who the face(s) of the company is/are.
