They're both virtual computers. They (one or the other) run in Linux (the operating system in Android phones), and the apps run in the virtual computer.
ART (Android RunTime) should run apps faster, but some apps written to take advantages of little tricks available in Dalvik won't run on ART. (Dalvik is named, by the man who wrote it, after the village of the same name in Iceland.) (Every operating system has little thngs that developers discover that weren't intended to be used in the way they use them. Writing another operating system to run the same apps often overlooks these little "hidden hooks". Rooting depends on little hidden things in either Android or Linux.)
So the only problems you might run into are apps that won't run in ART. And the performance improvement won't be fantastic, it'll be anywhere (depending on the app) from nothing to "oh, it seems to be running a little faster". I wouldn't bother yet.
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