The lead changed hands several times Tuesday as Exxon Mobil (XOM) recovered from early losses and Apple’s (AAPL) gains leveled off. By 3:00 p.m, Apple’s market capitalization (share price times number of shares outstanding) was more than $5 billion larger than Exxon’s, according to Google Finance. As the closing bell approached, however, Exxon surged faster than Apple and retook the lead.

Apple closed at $374.01, up $20.80 (5.89%) for the day. Exxon closed at $71.64, up $1.45 (2.07%). That put Exxon’s market cap ($348.32 billion) slightly ahead of Apple’s ($346.74 billion).

Apple became the world’s most valuable technology company when it passed Microsoft (MSFT) in April 2010. On Tuesday it became, at least for a few hours, the world’s most valuable public company in any field of business.

UPDATE: Apple re-overtook Exxon Mobile in early trading Wednesday. See here.

In the fall of 1997, Michael Dell was asked what he would do if he were CEO of Apple. He answered that he would shut it down and give the money back to the shareholders (link). Today, nearly 14 years later, Dell (DELL) is worth $27 billion and Apple is worth 12.7 Dells.