Moore had trouble with deadlines
According to an interview with Kirkman:
Q: You and artist Tony Moore are longtime friends and collaborators. You
created The Walking Dead comic together. What prompted Tony to leave
the series? Any drama, I hope?
A: Well, there’s always drama when people
as close as Tony and I work together. So, you know, sure. My favourite
response to this question is that Tony got pregnant and had to leave
the book, because that leaves things interesting and mysterious which
is the best way to leave them.
The real answer is much more boring. We were very adamant about
scheduling early on, and Tony—fantastic artist though he is—is much
more the type that works best on a variety of projects, rather than a
single, constant deadline, so we decided it would be best if we went
our separate ways for the time being. So, at that time, I contacted
Charlie Adlard, who is a fantastic artist, and we’ve been working
together ever since.
The darkness of Adlard's style may have better suited the comic
There are two other possible contributing factors.
Robert Kirkman, creator of The Walking Dead, has stated that Adlard's style is better suited to capturing the "mood" and "eeriness" of the series.
When asked about the artistic switch from Tony Moore to Charlie
Adlard, Kirkman replied:
"Tony and Charlie both do a great job portraying the characters
emotions and expressions, as well as drawing some mighty cool zombies,
Tony especially—I think that guy kills people and keeps them in his
basement for reference. Charlie, I think, adds an additional layer of
mood and eeriness that Tony wasn't really bringing to the plate. This
book just keeps getting darker and darker and I think Charlie came on
the book at the right time for that. I think Charlie's stuff makes the
book seem more "serious" somehow. Both artists do a great job, though.
Tony's covers are spectacular and Charlie blows me away with every
issue he turns in."
While this is stated in terms of Adlard "coming in at the right time" for a shift in tone, some of the language makes me suspect that this was one of the reasons for bringing him on. For example:
"...an additional layer of mood and eeriness that Tony wasn't really
bringing to the plate."
Kirkman and Moore may have had a falling-out
According to Kirkman, in an interview with Marc Maron:
Kirman: “Yeah, it’s definitely an unfortunate thing but I think like, uh, I
don’t know. I still love the guy. If he called today and said he
needed a kidney, like, there’s a history there. It’s like real, you
know? But yeah, we definitely drifted apart. So, you know.”
Maron: “Over the show?”
Kirkman: “Over the comic. That six issue break was a pretty, uh, defining
moment in both of our lives.”
Moore later filed a suit, claiming that he (as co-creator of The Walking Dead) had been deceived into giving up his stake in the work. Although the suit was not filed until 2012, from what Kirkman says in the preceding quote the "drifting apart" may have happened earlier, during the run of the comic. This is, of course, not inconsistent with the idea that Kirkman judged Moore's art style to be inappropriate for the direction the comic was going.
As evidence that the hiring of Adlard itself likely was acrimonious, an interview with Moore:
Q: If you were on a boat with Kirkman and Charlie Adlard and you and Adlard fell out of the boat and were drowning, who do you think
Kirkman would save?
A: Charlie is clearly much more useful to him. I'd wager I was pushed out of the boat in the first place.