Veitch had already developed a unique comics voice before he came into contact with Alan Moore. He produced some great comics for Marvel's Epic line, including The One.
He'd go on to work with Moore on his legendary Swamp Thing run, as well as a couple issues of Miracleman. He'd go on to write Swamp Thing after Moore left, before he had his own falling out with DC Comics.
From Wikipedia: "When Moore left the Swamp Thing series after issue #64, Veitch took over as writer, dividing art duties between himself and Alfredo Alcala. His Swamp Thing stories took a similar approach to Moore's, combining horror-fantasy, ecological concerns, and an encyclopedic knowledge of DC Comics fantasy characters; he gradually turned his attention from the DC Universe to history and mythology, using time travel to introduce his hero to a variety of legendary figures. This was to conclude in issue #91. Difficulties arose after Veitch's plan for issue #88, a story in which Swamp Thing met Jesus Christ, was scrapped by DC President Jenette Kahn. Although DC had approved Veitch's initial script for the Jesus story, the topic was later deemed too inflammatory and was cancelled at the last minute. The publisher and writer were unable to reach a compromise; Veitch quit, and vowed never to work for DC until the story saw print."
He'd go on to work with Moore on 1963, Supreme and Greyshirt from Tomorrow Stories. He's done a ton of work since.
He's also got a great blog going here. On one post about the secret development of Marvel's The Sentry, he talked about the nature of the retro work he did on 1963 and Supreme:
"I’d been involved in two major retro projects (1963 and SUPREME) in which Alan Moore and I had developed a sort of “deadpan” approach to the genre. Then and now, most retro stories you see tend to be over-exaggerated. The dumbness is caricatured; played for laughs in both the writing and art. Alan and I believed such an approach was to be avoided; that in fact the mad random lunacy of a Mort Weisenberger SUPERMAN or a Lee/Kirby THOR needed no exaggeration at all. It was this close-as-you-can-get-it mimicry approach that I wanted to bring to SENTRY..."At the time, he was also selling Supreme pages: