I've got one of those Zoom h4 recorders and while it's good in some situations, I find it's very noisy and the mics are just "ok". Certainly not bad, but if cost was no concern, I'd much rather a proper set of independent mics I could use with whatever recording setup. Any amount of hand movement or wind makes it unusable. I haven't tried it with external mics though- but that's not really the original question.
I don't have a ton of experience with different mics to draw from, but the flattest sounding (in a good way) mic I've tried to far is a CADm179. It's a very "boring" sounding mic, but has always done a good job of picking up whatever I'm actually hearing. I have some of the basic mics that bands tend to use (57, 58, etc) and some Rode mics, as well as I've rented a bunch for different reasons, but the CAD is the one I go to whenever I think "I want to capture the thing I'm hearing right now".