Well whoever from "The West" had got involved in a military strike to punish Assad and degrade his military facilities would be pretty embarassed, politically and diplomatically speaking, one would imagine.
The Russians and the Chinese would no doubt lead the way and try to marshall and international response to capitalise on that embarassment to create whatever political, diplomatic and economic advantages they could, and it would further undermine the USA's authority as the flag-bearer for democracy on the world stage.
Not sure that it would be "an even bigger mess up for the West than Iraq though". Iraq remains a special case so far. An invasion with the objective of regime change, justified by the use of false intelligence, resulting in the deaths of 100s of thousands of civilians and a country in ruins with little or no plan on how to manage the reconstruction is much much worse in my opinion than the current notions being circulated of some kind of limited missile strike on Syria