There are plenty of names I could've chosen for this case study, but I tried to stick to fantasy-worthy and mix in some studs and some marginal pitchers. My goal is to analyze the movement of pitchers between leagues and see if I can quantify some type of trends. Here's what I found:
Randy Johnson: The Big Unit actually began his career in Montreal, but the stint was too brief to offer any insight into his pitching. He was very good in Seattle, consistently striking out 200+ per year and breaking 300 K's once (in 1993). After moving to the NL - first Houston, then Arizona, he saw his strikeout totals increase dramatically. He had five straight seasons well over 300 strikeouts, beginning at age 34 and ending at 38. The strikeouts cannot be explained by ballpark factor, and it's unlikely he was gaining any velocity in his mid-30s, suggesting Johnson definitely benefited from facing NL lineups on a yearly basis. He struggled in his return to the AL as a Yankee, and pitched better in limited action after returning to the Diamondbacks (significant K/9 increase, and lower ERA despite higher BABIP). Johnson is one who benefited hugely from moving to the NL from the AL.

Pedro Martinez: Pedro began in Montreal, moved to Boston, and eventually returned to New York. He was a fine pitcher until his last season in Montreal (1997), at which point he became dominant. Still, his WHIP and ERA dropped when he reached Boston (his WHIP was under 1.00 in 4 of 7 seasons with Boston), and strikeouts increased, though less dramatically than Johnson. He faded quickly as a member of the Mets, and has been fighting just to stay on the field. Pedro is just the opposite of the Big Unit - he was a significantly better pitcher during his time in the American League.
Roger Clemens: His name certainly belongs in baseball lore. Clemens had a renaissance late in his career that few, if any, have ever equaled. The fact that it coincided with moving from New York (AL) to Houston (NL) may have helped, but there is reason to believe chemistry had as much to do with his statistical improvements as changing leagues. Still, he posted a huge drop in both WHIP and ERA after moving to the NL at age 42.

Andy Pettitte: Clemens' friend, who followed him to Houston, had some success in moving from AL to NL. He had the best year of his career with Houston in 2005, posting career lows in WHIP, ERA, and BAA. He also didn't walk many batters at all. He followed that year with a miserable one, and has improved from his pathetic '06 since returning to the AL (decreasing ERA & WHIP, increasing K/9). So although Pettitte did have his career year in the NL, he had bad seasons in his other year and a half, and he's improved since returning to the Yankees.
Bronson Arroyo: Arroyo is often cited as the ultimate case of a pitcher benefiting from moving leagues. After switching from the brutal AL East to the weak-hitting NL Central, he went from being a below-average pitcher to a very good one. He has since returned to Earth, however, suffering from a steadily increasing WHIP, ERA, and BAA. His 2006 year may have been partially from changing leagues, but the move to the NL doesn't seem to have permanently helped Bronson Arroyo become anything more than a mediocre major league pitcher.

Ted Lilly: Lilly moved from Toronto (and Oakland and New York before them) to the Cubs in 2006, and benefited from the move. The most noticeable benefit came in terms of his walks - his BB/9 ratio was cut nearly in half after he moved into the NL Central. (For comparison purposes, Arroyo - who made the same divisional leap a year earlier - had a virtually unchanged BB/9 ratio). His WHIP has dropped and K/9 has increased as well over the two years Lilly has spent in the NL. He's definitely become a better pitcher after moving to the NL.
Jamie Moyer: Moyer, the ageless wonder who is currently pitching for Philadelphia, moved from Seattle to the NL East in 2006. Since then, he's a had a slight statistical renaissance - his K/9 has gone up, and this year especially he's had a stellar drop in ERA. His numbers would be more impressive, except that he plays in perhaps the most hitter-friendly park in baseball. The move to the NL has probably helped him a little in the late stages of his career.
With all these examples, what can I conclude? Well, unfortunately, very little. Johnson, Clemens, Arroyo, Lilly, and Moyer all saw some boost from moving to the NL; I call Pettitte a wash, while Martinez benefited substantially from moving to the AL. Arroyo's boost was temporary, Clemens' was perhaps mitigated by other circumstances, and Moyer's has to be qualified by a ballpark rating. As owners of Johan Santana, who were looking for 300+ strikeouts this year, already know, moving from one league to another doesn't guarantee much of anything for a pitcher.