I remember as a kid I automatically went with the variable weapon damage optional rule given in the Moldvay Basic set. I know my rational was that it "only made sense" that a sword would do more damage than a dagger.
However, as I get older I appreciate the standard rule that every weapon does 1d6 damage. When I read the OD&D 3 Little Brown Books, I began to see the fact that normal men have 1d6 hit points and every weapon does 1d6 damage as an elegantly symmetrical system. And as pointed out by Philotomy on his excellent website (http://www.philotomy.com), "This makes perfect sense given D&D's abstract system: a dagger thrust can kill you just as readily as a chop from a greataxe."
I my mind keeping with this system is a definite plus for the Swords & Wizardry Whitebox version available at: http://www.swordsandwizardry.com/whitebox.htm
In B/X the same symmetry does not exist. Normal men get 1d4 hit points (B40). So even using the standard 1d6 damage for every weapon, on average each hit will kill a normal man. However, you also have to remember that in OD&D monsters, in general, also had one attack per round which also did 1d6 damage. In B/X, many monsters get multiple attacks and do various ranges of damage. So I am wondering if by keeping with the standard weapon damage of 1d6 whether one puts the PCs at a disadvantage. My guess is that most players would also view the standard d6 damage for each weapon as "non-sensical" and would prefer the variable weapon damage.