Biggio had some ridiculous years in his prime, just look at his 1998 season:
.325 AVG, .403 OBP, 24 HRs, 88 RBIs and 50 SBs
Pedroia could potentially match all of those with the exception of the 50 SBs obviously. But while Pedroia doesn't have mind-blowing speed, it wouldn't shock me to see 30 SBs out of him. The ability to steal bases isn't so much based on speed as it is knowledge of the pitcher and catcher and the ability to recognize tendencies. You saw that with his jump from 7 SBs to 20 in one year
Aside from all that, Pedroia should end up with better than Biggio's .281 career average and be right around his .363 OBP mark and 17-63 HR-RBI season average. 20 seasons with the same organization is incredible though...
in terms of fielding, Pedroia could easily get 4 gold gloves like Biggio did, especially considering he's already established his gold glove-caliber reputation at just 24 years old but Pedroia will never have the versatility of playing the outfield like Biggio did