Q. When should we use plano-convex lenses, and when should we use bi-convex?

As I had the same question from Jenne and Dmass in a month,
I just like to introduce a good summary about it.
Lens selection guide (Newport)
http://www.newport.com/Lens-Selection-Guide/140908/1033/catalog.aspx

At a first order, they have the same function.
Abberation (= non-ideal behavior of the lens) is the matter.