If the show had stayed with the original power of three and Prue didn't die, how would the show have been different, I dont think anything major would have happened, the only season that would get a big makeover is season 4, and all Paige centric episodes would become Prue centric.
Prue and Piper would be trying to rescue Phoebe from the underworld after her deal with The Source, so I guess we get evil Phoebe earlier, or she gets rescued and doesn't become evil yet and the original Source is killed at the end of season 4, and Cole dies mid-way into season 5. As for Prue's love interests, no idea who they would create or pair her with, maybe Bane returns, or Andy is resurrected as a whitelighter after Leo becomes human, giving Prue a happy ending in the last season.
However the final season instead of the ultimate power being Billie and Christy, what if it was instead Paige, and they decided to introduce the lost sister, so basically its the charmed ones trying to find Paige who was captured by demons, and not Billie finding her sister or she just discovers them during Still Charmed and Kicking when they are presumed dead, after trying to find her lost family. Prue being in season 8, theres no way she would handle Billie one bit, she would not forgive her in Forever Charmed, and would of probaly killed her if she happened to survive the explosion in Kill Bille Vol. 2, but I do like the idea of having Paige in season 8 introduced instead of Billie, if we did have the original power of three for the entire series. Maybe Paige could be hinted at in earlier seasons, so not to just bring her out of the blue in season 8.