The owl looks great, lots of great textures and colors, I would definitely try to improve the branch make the letters less cartoony and ake them look like wood, i would also tone down the green on the leaves. But it looks pretty awesome.
I really like the colors. Maybe pull the green in more by adding it to the font or his eyes somehow... I would sharpen the edges on the font making it more square than round. The shapes that make up the owl are pointed...if you did the same with the font, they would compliment each other very nicely.
Man that's cute. It's so cute it's hard to critique! I'm not sure what the white is on the beak, I'd maybe get rid of that. And I think owl ears most of the time angle a bit outwards rather than inwards. Very awesome tho, I love it!
Nice work. Maybe try working on the transition between your thick outer line and the feathers. Right now I don't really feel like they flow very well. Also, I would exaggerate the "hoot" to make it look more like a branch. Good work, though.
Could you critique mine as well? I have an owl, too :)