No, Bieksa is simply taller. Height is not the same as size. Shea Theodore is 6'1". Are you going to say he's "bigger" than Beauchemin? In hockey, size is also mass. As in, muscle mass. You can be pedantic, and say that Bieksa is bigger, simply because he's taller, but where it actually matters Beauchemin is the stronger player. He's bigger. He isn't taller, but he's bigger.
You mean the analysis that suggests Beauchemin is better defensively? That Beauchemin was relied on more heavily in defensive situations, and did well in those situations. At least in Anaheim. Bieksa, on the other hand, looks as if he was used less heavily, and hasn't been as good with the opportunities.
A big part of it? He was 5th, amongst their defensemen, in SH TOI. That puts him just behind Luca Sbisa, for the record. I'm certain Bieksa was a part of it, but a big part of it? The evidence doesn't really play that out. In fact, the last year Bieksa was top 2 in shorthanded TOI on his team for defensemen was 2011-2012.
So, while your argument regarding the difference in SH ice time is statistically true, it's also misleading and inaccurate. All you need to do is look a little deeper, and you'd see that Bieksa was not as heavily used for Vancouver as Beauchemin was for Anaheim. That does matter, when you're trying to make points about goals against, and the like. Hockey is a team sport, and Bieksa was a 2nd unit PK'er, on a superior PK'ing team, while Beauchemin was a 1st unit PK'er, on a fairly average PK'er team. That doesn't necessarily place one player over the other, but I'd have a difficult time labeling Bieksa as a better penalty killer when he was used in a lesser role on a better penalty killing team. Not only were Bieksa's responsibilities less, but hockey is a team sport, and players will benefit, or suffer, from team issues. Special teams are a team issue.