I can't really compare them because the gyazo screenshot is zoomed in.
However, quality always depends on what your resolution settings are and how you're saving the image. I don't have GIMP so I'm not sure exactly where you would go, but since it's compared to Photoshop, I'll explain it that way and maybe you can find it in GIMP.
When you're creating a new image/canvas, it allows you to adjust the resolution from the get:
You should be able to go in and edit the resolution settings at any time before you save the image. 72 is default on photoshop and I usually bump it up to about 100 and sharpen the image just a tad for imvu icons, but won't go higher than 300 for any image. Higher resolution = bigger files size, and since you're making an icon, IMVU won't let you upload it if it's over 50kb.
Saving the image as a .png will keep the quality of the image. Saving it as any others, such as .gif, .jpg/jpeg, etc. will compress the image.
I know a lot of people use GIMP because they can't afford to buy photoshop, but photoshop cs2 is free if you ever wanted to play around with it. (Click for download link.