Difficult to say how much the difference will be noticed because so much depends on how the tool is used, but drilling 12mm holes in stainless suggests bigger would be better.
Drilling mild-steel, a .33HP motor will take about 1½ times longer to remove the same amount of metal as 0.5HP. In theory 0.33HP will just take a bit longer to do the same job, which if often not a problem.
However, the effect of reduced power on Stainless steel is trickier to predict because many stainless alloys work-harden. Misery ensues when a tool fails to cut stainless due lack of power or torque! In consequence more skill is needed to cut work-hardening metal with a tiny motor than a big one, because big motors can power through minor problems like a slightly blunt drill or wrong rpm or feed-rate.
Discussing the power output of motors, it's useful to understand the power claimed on the motor plate isn't an absolute limit. Idling electric motors deliver much less than their rating, whilst heavily loaded electric motors can deliver much more than the plate rating. But not for long – the windings overheat and out comes magic smoke!
Thus the physical size of electric motors is a weak indicator of power output. Old motors are physically bigger than modern ones because the enamel used to insulate golden age magnet wire is much less heat proof than modern enamels. And to prevent micro-holes in the insulation, older enamel was applied thickly which reduces the motor's efficiency. Old motors have to be physically big to keep cool, whereas modern equivalents run considerably hotter and 10 to 20% more efficiently. Duty cycle is also a major influence on physical size: a motor delivering 1HP but only run for 30 minutes in every hour can be made much smaller than a motor designed to output 1HP continually.
My guess is the Boxford's original motor was rated for continuos hard work in a busy professional workshop. In comparison most home workshops are a holiday camp! There's a reasonable prospect a 0.33HP motor can occasionally be flogged hard enough in a home workshop to replace a 0.5HP unit, but bear in mind the drill's original 0.5HP motor was probably called on in the same way to deliver more power in bursts. A small motor isn't as capable as a big one.
Personally I'm nervous of re-using ancient electric motors of whatever power. Age, overheating and damp are all unkind to electrical insulation and the metalwork inside may be corroded too. Single-phase motors are extra vulnerable because their capacitors and centrifugal switches also degrade over time. As few of us have the facilities to do a proper insulation test there's much to be said in favour of upgrading to a new 3-phase motor and a VFD. 3-phase motors have better torque performance than single-phase motors too. No one regrets replacing single phase motors!
Dave