If they never accellerate or decellerate, their laptimes will be equal.... the low polar moment of inertia kart will accellerate more quickly, but also decellerate more quickly, while the high polar moment of inertia kart will respond more slowly. Theoretically, the low MOI kart should take off better from the start, then the high MOI will lose less when they let off for the turn. Which is faster?? Kinda' depends on the track type and how much time is spent off / on throttle. It also bears mentioning that the "flywheel effect" is negated if the clutch disengages while coasting, so the low MOI kart can keep the accelleration advantage with an appropriate clutch setting.
Similar to how a heavy driver can win a mid weight class if it's a wide-open track with no cautions, high MOI karts have to have the right conditions to excel. The difference in analogy is that rotational weight is magnified in effect compared to static weight. Rotational MOI also has more to do with mass than its' derived component of weight, but since they're related, most go by "weight". (it's easier to stop a kart tire from spinning in outer space than a car tire, though both are "weightless" -- it's the mass you're acting against, and therefore whatever you can do to reduce mass = good.)
I'm kinda' surprised that nobody's using carbon fiber, titanium, or magnesium rims in LTO racing... ditto for sprocket hubs, brakes, brake hubs....etc. etc.
Since FORCE = MASS x ACCELLERATION, get the most HP to boost ACCEL you can reliably stand , then working on reducing MASS, first rotationally, then overall. Add weight back on as needed to balance kart.