The amateur analysts who follow Apple (AAPL) tend to be considerably more bullish than the professionals who do it for banks and brokerage houses. After all, unlike the sell-side analysts who are telling investors to buy the stock, they don’t have clients who will be angry and disappointed if the company doesn’t exceed expectations.

But with Apple set to report its fiscal first-quarter earnings Tuesday, the gap between bloggers and pros is as wide as we can remember.

Among the 44 analysts we polled in advance of Tuesday’s Q1 2011 earnings call — 10 amateurs and 34 professionals — the difference in their consensus revenues, $26.4 billion and $24.31 billion, respectively, was nearly $2.1 billion (8.6%). In percentage terms, the gap between their EPS estimates — nearly $1 — was even larger: a whopping 18%.

The prize for most bullish estimate goes to Dennis Hildebrand of Apple’s Gold, an amateur with a mixed track record who is predicting earnings of $6.61 on revenues of $27.8 billion.

The most conservative estimate comes, ironically, from Needham’s Charlie Wolf, a long-time Apple bull. Wolf, who’s calling for earnings of $4.93 on revenues of $23.01 billion, tends to come in on the low side. He explained in a private e-mail that he rarely changes the numbers he files immediately after each quarterly earnings report, and he bases his calculations on Apple’s (invariably conservative) gross margin guidance.

Below: The revenue, EPS and gross margin numbers we’ve gathered so far (amateurs in blue, pros in peach). The Deagol rating in the sixth column is a measure of each analyst’s accuracy over the past two or three quarters, with 1 the highest and 40 the lowest. (See here for an explanation for how it was derived.)

See also:

• Earnings smackdown: The best and worst Apple analysts (Q4 2010)
• Mac zigs while the PC market zags
• iPhone sales in the AT&T era
• How big was Apple’s iPad Christmas?

[Follow Philip Elmer-DeWitt on Twitter @philiped]