Does driver length influence ability to square club face?

Curious to hear everyone's thoughts.  I'm using two drivers right now: an SLDR set at 9.5*, 45" long, and a Big Bertha DBD set at 10.5* with a stock shaft (think it's 45.5" or 46").  Played 9 holes this morning and hit one tee shot on every hole either each driver.  Noticed that they all seemed to start on the same line (except for the ones with terrible swings of course), but where the SLDR drew back on every shot, the DBD seemed to stay straight about half the time, amounting to about a 10 yard block.

I think these clubs are roughly equal in terms of forgiveness, and I have no problem elevating the ball and generally hit the center of the face.  Could the extra length of the DBD make it just a wee bit harder to square up?

Probably going to cut it anyway, but interested to hear opinions.

All other things considered equal, I absolutely think so. But it is a strong hunch at best on my personal experiences. Never hit a driver then hit it again after shortening it, which in my opinion would be the only 100% confirmation. But other things happen too; a shorter lighter driver can make you a tad bit more handsy so I would cut half inch at a time at the most.

Let us know how it works out. I am certainly curious.

On account of it being a holiday wkd (and my overall lazinesses today), just ran to the local range to confirm.  I was somewhat mistaken, the BB definitely starts right of where the SLDR starts.  Same dispersion though.  Mostly draws with the SLDR, half draws half blocks with the BB.  Interestingly the SLDR is likely set a bit open, since it's a 10.5* that I've dropped down to 9.5*.

Think the torque is pretty close: Aldila Rogue Silver 60 stiff in the BB (3.4 torque) and GD AD-DI6 S in the SLDE (3.3 torque).  I've always loved the DI 6 shaft, so maybe that's it.  Could try swapping that out of the SLDR and putting in the BB.  Would be hard to do side by side comparison though obv.