What is the advantage of a "compact crankset" vs changing a chainring?
Getting though all the hype and testosterone - Compact cranks allow a smaller small chain ring as they have a smaller BCD. Modern tech means you can have a wider gap between chain rings, giving larger spread.

This means modern compact cranks with wide range 11 or 12 speed cassettes can get the same gear range and stepping as a triple 7 or 8 speed with just a double. 

Where you would switch to a compact is if you have decided you need a smaller chairing than will fit on a standard crank. However, you may still need a new Front derailleur and possibly a shifter.