When it comes to graphic novels(English), these are the two best writers  in my opinion.

Frank miller started off with DareDevil, a character whom he took from a second string hero to the heights of popularity. Some of the themes had a manga influence( Miller is a huge "Lone Wolf and Cub" fan).Then, in 1986, he created the crowning gem of super-hero graphic novels,and arguably the best graphic novel of all times, The Dark knight returns, followed up by the equally impressive(maybe more critically acclaimed) Batman Year one.  The 90s brought out another masterpiece by him, Sin City( made into a good,albeit overly stylised, movie)

Havent read the entire body of work by Alan Moore, but what ive read impresses me more and more with each re-read. Has a style which is very different to the stylish, noir style of Miller. Reading his work makes you feel like youre really reading a master story-teller, and his best works(V for Vendetta and Watchmen ) have deep social and philosophical messages, reducing their accessibility but allowing them to transcend genres. League Of Extraordinary Gentlemen is as pure a fun comics as you can ever get(with rich references to Victorian Literature).And the back end of his works is brought by From Hell, Promethea etc

so, who is better, in your opinion, and why?

Miller wins because of Watchmen

My nod goes for Miller, he doesn't seem to want to force his message on you with ever syllable he writes. Not to say he doesn't have one, of course, but he is much less preachy than Moore.

Although I would put DKR and Watchmen as a solid tie for second best graphic novel, with the first place honors being split between Bone (I count the whole series) and Death: The High Cost of Living.

I would put Ennis above Miller. I think Preacher is the greatest long-running series of the past 20 years.

As for Moore, no one even competes on his level. Read his early Swamp Thing stuff and it's amazing to see what he was doing way back in the day. Then he did Watchmen, V for Vendetta, From Hell, etc. and just made everybody else look bad.

Still, this isn't an insult to Miller at all. He's in my top five list of comic writers easily. He just has a lot more superhero stuff under his belt than Ennis or Moore, which limits his scope of storytelling a bit.

Wait... You call Moore preachy and then prop up Death: The High Cost of Living, the originator of the whiny emo book genre? Death was good, but I found parts of it insufferable and definitely not on the level of Watchmen or a handful of Moore's other work.

Props to the Bone nod, though. Bone was bloody freakin' brilliant (though the last few trades didn't live up to the earlier work... I let it slide because it was almost impossible to live up to the first two trades in that series).

Did you mean Moore?

Either that or he really hated Watchmen. 

 I believe i did. Damn

@rocketpig
Where would you rank Sandman as a long running series?
i read it recently and felt that it was brilliantly written, especially the depiction of the Endless.For me the third after these two would be Neil Gaiman, though i havent read Preacher yet

I went off and on with Sandman... Honestly, I can't rank the series. I would pick up a few issues, get interested, and then trail off again and ignore it for awhile.

I should probably read the whole damned thing one of these days.

Has Gaiman really done any books since The Sandman?