I've read all of Cook's Garrett series and all of Butcher's Dresden series (except the most recent one) and I enjoy them both. Of the two I find Cook's work much closer to film noir in style, while Butcher is modern detective in style. Garrett is in a total fantasy world, particularly the city of Tun-Faire while Dresden is set in the city of modern Chicago and environs. Both work very, very well.
Cook takes the classic fantasy themes and adds his own fun modifications and though he has a sense of grittiness to his stories, Butcher is darker though very intruguing and I find his plots and characters very compelling and Dresden's enemies nothing to be triffiled with --never. The fairies... well I won't give it away and the vampires are... well I won't give that away, either.
They are also both in first person voice which is my absolute favorite way to read a story.
It is essential that you start with book 1 and proceed from there because there are common threads, themes, and information that carries throughout both series.
I thought Cook really became weak in his next to last offering in the Garrett series, but his last release seems to have gotten back on track.