They are separate franchises, but Warner Brothers wanted this to happen and it's clearly intended to be a crossover.
Arrowverse is only Earth-Prime to the Arrowverse. That term is relative. The DC Extended Universe could be the new Earth-1.
No ones saying that the Arrowverse is better than the DC Extended Universe or anything.
On the Paragons, there are multiple of each, considering Earth-167 and Earth-97's Supermen both being considered a Paragon of Truth. This means that Earth-DCEU Batman could have been the Paragon of Courage, who would have made Batwoman look like chewed chewingum in a fight, Wonder Woman could have been the Paragon of Love, which fits her progression more than Barry Allen, Superman for hope, which fits the original plan for his character, Aquaman for honor, Shazam for destiny, Cyborg for humanity and the Flash for... truth?