Could it be that the
COMMON.WEALTH variant was set up to mark this as a trial of an alternate style of A which was only used in 1652. A COMMON.WEALTH die with the typical style A was subsequently used in later years - 1656.
Which obverse die is rarer is a good question - intuitively one might guess the die with the alternate style of A would be the rarer type as its use seems to have been abandoned after 1652..
The story does not finish there however as in 1654 a variant of the letter V and W both with rounded corners reminiscent of the A which failed, started to appear on coinage, but not always together..