Market Capitalization is a simplistic method based on current stock price and doesn't solely determine the "worth" of a company (for say a merger or acquisition). If that were the case, Home Depot with their current market cap of 310 billion should be worth 2.6 times Lowe's. It's not that simple. Additionally, if a company were to suddenly file for bankruptcy and be forced to liquidate all their assets and settle all their debts (at full value), I can assure you what most would have left over will be nothing close to their previous market cap high.
It's a documented fact that for a long time Sears Holdings Corporation burned through billions upon billions of their cash reserves trying to keep their stock price high (Sears highest stock price was $193 back on April 17, 2007) and had they only invested that money into the actual business they may very well have had a different outcome. Lowe's is in fact following much of that same Sears playbook. And while Lowe's is making investments within the company many would argue that the value of those investment are falling well short of what Lowe's is spending and well behind what Home Depot is consistently accomplishing. Time will ultimately tell who is the leader and who is the follower.