KNIT:  When you're working in stockinette stitch (knit a row, purl a row, unless you're working in the round - all knit or all purl, then), the knit side looks like many little V's all stuck together. A few people knit their warmers in this way, probably a few casts. When you do a lot of color changes, the knit side will look "cleaner" - there will be more clear definition in between the two colors. 

PURL:  I myself prefer purl side out (unless I'm working from a reference picture that is clearly knit side out). This side looks like many little bumps. When you do color changes, this side tends to look a little messier - a little more "organic". For example, if you knit one row of a different color, on the knit side it will look like one row of the different color. On the purl side it will look like two rows of the different color mixed in with the main color.

GARTER:  However, there is also garter stitch, which is all knit rows or all purl rows (unless you're working in the round, in which case it's knit a row, purl a row). This will also give you the sort of "organic" look the purl side of stockinette gives you, but I personally don't use it. Certain knitters achieve beautiful warmers in garter stitch - but they use thin yarn and small needles.