Size by employees misleadingly favors retail outlets and government; just like market cap unfairly favors companies with inflated stock prices. Revenue favors companies with enormous line-item purchases (like Oil companies) and profit ratios may as well say "list of largest tech companies".
At the end of the day there's no one metric that can tell you the "size" of a company, because the term is too broad.
Size by employees is a terrible metric. Market cap isn't perfect but it is the company's actual value after all. Revenue and profit are more imperfect, IMO.
Most simply, value is a non-fixed inherent property that can change depending on the asset / liability and the entities involved. A valuation is an actual estimated value given some conditions.
Simple example: Celery has no value to me, because I find its taste disgusting. However, I happily pay for bundles of cilantro, which in turn have no value to others that find its taste disgusting.
In the case of a publicly traded company, the conditions are "if all shares were immediately liquidated at the current price". In the case of a company buying that publicly traded company, an actual value can be arrived at, due to having a fixed set of assets, liabilities, and participating entities. And, as you pointed out, those two numbers rarely match up.
