In a nice explanation for where Awesome was going to go, in a post-Image/pre-Awesome press release, Rob Liefeld explained the decision as a moving away from the darker elements of Extreme:
This is from the 11/27/96 Diamond Dateline. EXTREME ANNOUNCES NEW PHILOSOPHY FOR 1997. Extreme Studios-whose books will now be published under the Maximum Press banner-has announced that its 1997 publishing plans will embrace a new philosophy designed to reduce the amount of graphic violence, language, and adult/mature situations that have characterized several of its titles. "For the past two years," said Extreme Studios President Rob Liefeld, "I have watched our titles and the subject matter they contain grow darker and darker...I feel that we've gotten way too close to the edge and it's time to pull back." Liefeld continued by citing the bold, bright books that influenced him as a young comics reader, such as The Legion of Super-Heroes, The Teen Titans, The Avengers, and X-Men. "When I look at our current slate of titles," he said, "I don't see the same attributes that attracted me as a fan." Liefeld assumed responsibility for creating so many books which glorified the dark side of human nature, such as Priest, Prophet and Avengelyne. "While we realize there is a segment of fandom that craves the dark side," he said, "we feel that shifting our focus towards a lighter, less menacing tone is the right move for our company." To that end, Priest, Darkchylde, and Celestine-Extreme books that, in Liefeld's view, "explore and promote evil"-have been canceled. Avengelyne, which Liefeld defined as a character fighting for good, will be toned down and made more accessible for younger readers. Other Extreme titles-such as Youngblood, Glory, Prophet and NewMen-will become more prominent in the company's line-up, starting with the release of Extreme Genesis #0, which will introduce readers to these books and explain how they exist outside the Image Comics Universe. (Previously scheduled for a January 1997 release Extreme Genesis has been rescheduled for February.)
As I talked about before, I believe Extreme Genesis was what eventually became Judgment Day.
(UPDATE: 5/8/18 - So my friend Rob explained that Extreme Genesis was not Judgment Day, but was a planned crossover among all Liefeld's comics, which at the time were being printed under the Maximum imprint, and would see the heroes 20 years in the future. However, some combination of Moore's Judgment Day plan, acquiring the license to Fighting American, and the offering of a lot of investor money made him abandon Extreme Genesis and the Maximum branding and create Awesome.)
Now Liefeld didn't completely stick with this pledge, as we'll see with Menace, Chapel and some of the other odds and ends that Awesome would put out (and that I'll talk about in a post later), but Awesome did put together a few titles at the launch of the company that were supposed to capitalize on this more broad-based appeal. Beyond Supreme, the other three main titles were Coven, Kaboom and Fighting American.
I've been reading them and will do separate posts about each series as well as a post about the other odds and ends Awesome somehow managed to let escape into the world. One consistent for all of these three other main series was their writer: Jeph Loeb.
One of Liefeld's coups in starting Awesome was to lure Loeb to come and be his publisher. Loeb, who wrote movies (Teen Wolf and Commando? Seriously, how did I not know this about Jeph Loeb before this?) and television (Smallville, Lost and Heroes), was doing very well in comics by the mid-'90s, having written Batman: The Long Halloween, for which he'd win an Eisner award. He also happened to have teamed up with Liefeld on the Heroes Reborn series of Captain America for Marvel (more on that when I get to Fighting American). At the launch of Awesome in 1997, Loeb wrote each of the three series that Moore wasn't doing himself. Some of the series are good and some are a little forgettable.
Don't feel bad for Loeb, though. After Awesome, he'd return to DC to work on a little comic you may have heard of called Batman: Hush with some guy named Jim Lee. Questionable career move there Teen Wolf guy!