Ah, the irony. Bill Miller, the legendary mutual fund manager, is mystified that so many investors ignore the advice of Warren Buffett. Yet in some respects, so does Miller.

For example, one of Buffett's investing principles involves staying within his circle of competence. On computer-related businesses, the Oracle once said, "I don't know what that world will look like in 10 years, and I don't want to play in a game where the other guy has an advantage over me."

Miller may have a knowledge advantage over Buffett in the tech sector, but even he doesn't know what that world will look like in 10 years. Yet he's invested in companies such as eBay and DirecTV (Nasdaq: DTV), which operate in fast-changing arenas. Last year, he explained his DirecTV rationale: "The important strategies at both AT&T and Verizon (NYSE: VZ) have shifted to video, and we believe DirecTV could be a target of a takeover by either AT&T or Verizon in the next couple of years." That sounds suspiciously like speculation to me.

Miller has also stated that the market could gain 15% in the coming year. More than 30 years ago, Buffett said, "[S]uccessfully forecasting short term stock price movements is something we think neither we nor anyone else can do."

They're not so different
Still, both Miller and Buffett have favored insurance and other financial companies. Miller owns shares of Citigroup (NYSE: C) and General Electric (NYSE: GE), the latter of which derived $50.6 billion in 2009 revenue from its financial division. Why is Miller so keen on banks? As he explained: "The new financial-reform law requires banks to divest operations that trade for their own account. Those businesses are a major reason why bank earnings are so volatile. Without them, bank earnings will be much easier to anticipate."

Both Miller and Buffett also seek bargains, though they may define them differently. Miller scooped up shares of offshore drilling specialist Transocean (NYSE: RIG) after the Gulf oil spill, believing that "worries were overblown and the odds favored an investment at those levels."

In addition, both like to bet big. Miller has more than 7% of his Legg Mason Value Trust (LMVTX) fund in the power company AES (NYSE: AES). He pounced on it beginning in 2002, after Enron blew up and sent many power companies southward. In 2007, Miller explained, "The 2002 bear market saw some ... amazing prices. AES traded under $1. It will generate over $1 of free cash flow this year and is up 20 times from the lows of 2002."

Both Miller and Buffett have achieved great success. But now that Miller's legendary S&P 500-beating streak has ended, Buffett's approach has helped him hang on to more of his money. Miller might have avoided some losses by following Buffett more closely, but he'd also have missed out on some of his biggest winners.

We can learn a lot from both money managers.

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Longtime Fool contributor Selena Maranjian owns shares of eBay and General Electric. Motley Fool Options has recommended a bull call spread position on eBay, which is a Motley Fool Stock Advisor pick. The Fool owns shares of Transocean. Try any of our investing newsletter services free for 30 days. The Motley Fool is Fools writing for Fools.