I agree that trading up *can* be the right call, but in this case it's really hard to make that claim. The Falcons gave up a king's ransom to get him; enough that, if he ends up being anything less than Calvin Johnson-esque, it's a debatable-at-best move.
That's not an indictment of the trading-up philosophy (not entirely, anyway). It's more an indictment of how much they gave up, and that they gave all of that up to get a wide receiver.
To answer your question, the Falcons gave up the following: a 1st in year 1, 2nd in year 1, 4th in year 1, a 1st in year 2, and a 4th in year 2.
In 2006-07, for the Patriots, those picks became the following:
2006 1st: Laurence Maroney
2006 2nd: Chad Jackson
2006 4th: Stephen Gostkowski
2007 1st: Brandon Meriweather
2007 4th: traded for Randy Moss
In 2008-2009, they became:
2008 1st: Jerod Mayo (technically their 1st was forfeited due to Spygate, if you want to go that route, but at that point there's no comparison to be made)
2008 2nd: Terrence Wheatley
2008 4th: Jonathan Wilhite
2009 1st: Darius Butler, Brandon Tate, Julian Edelman, and Rob Gronkowski in 2010 (minus #190 in 2010).
Explanation for anyone who doesn't already know it: the Pats traded from 23 to 26, and from 26 down to where they picked Butler. In the process, they accumulated the picks that were used to pick Tate and Edelman, as well as the #44 in 2010. In 2010, #44 was traded along with #190 to get #42 from Oakland, which the Pats used to select Gronk
2009 4nd: Rich Ohrnberger
So even in the Patriots' worst-drafting years, you can make a very compelling case to take either of those hauls over Julio Jones. The 2008/09 group gives you Mayo, Edelman, and Gronk another year later, which is a no-brainer. I'd take Jones over the 06-07 haul, only because Moss fell off so quickly. Maroney, Gostkowski, and Meriweather were all serviceable, starting-caliber pros, though, so when you add those to the fact that one of those picks got Moss to New England, it becomes a very interesting argument.