Differences between KOH and phosphorus pentoxide as drying agents?
I found this page, which recreates information from Purification of Laboratory Chemicals, by Perrin and Armarego. It provides a qualitative ranking of drying agents, listing phosphorous pentoxide higher than KOH. The two drying agents work by different means:

KOH

Anhydrous KOH is hygroscopic. It absorbs water from the atmosphere. It much better at doing so than more common hygroscopic drying agents like calcium chloride or calcium sulfate (drierite). A pellet of KOH left out in a beaker or dish open to the air will have absorbed so much water vapor within an hour that it will now be a solution of KOH (that will continue to be hygroscopic, at least until the solution is 50% water). Calcium chloride and calcium sulfate only continue to absorb water until they reach their maximum hydration.

P4O10

Phosphorous pentoxide (really P4O10) is an anhydride of phosphoric acid. Phosphorous pentoxide reacts with water to form phosphoric acid: 
$$\ce{P4O10 + 6H2O -&gt; 4H3PO4}$$
Phosphoric acid is also hygroscopic and absorbs water to form a solution.

Since P4O10 is water reactive it is more difficult and dangerous to handle, especially for large groups of students. I might not use P4O10 if the substance being dried is very acid sensitive. Eventually, the vacuum will start volatilizing the acid. I might not use KOH for compounds that are incredibly base sensitive, although it is unlikely that KOH will sublime. In an undergraduate lab with multiple students, KOH should be fine if you want to save money and hassle.