I'm wondering if it is possible to change evince font rendering and make it render fonts like Adobe Acrobat Reader.
Evince uses default system fonts when they're specified in the document, and custom ones when they're embedded. This suggests that the problem may be with your font set. If this is the case, I suggest making sure that ttf-mscorefonts is installed and up-to-date.
Another possibility is that the document is using embedded fonts that may be corrupted or just didn't download properly. You can check the fonts by selecting "Properties" from the menu and the "Fonts" tab (I can't post an image because I don't have enough reputation...).
Other discussion of this issue have referenced other PDF readers, the most popular being Okular (KDE), xpdf, and epdfview. You may want to try one of these to see if you prefer them, but I haven't seen any clear solution to the question of why fonts would render better in any of these other applications than in evince.