Q: If you drift the corners, you can go less physical distance, but some speed might be sacrificed. If you stick the whole time, you maintain speed, but travel greater distance. So which one gets the faster lap, and why?
A: in kart-racing, or any other vehcile with tires since the way tires work is still the same: Drifting is slower... it is classic way to drive "fast in, slow out" which minimizes your momentum. But of course, it isn't that simple, because "stick" as you call it is not as simple as keeping the tires from sliding. Tires generate maximum grip when they are slipping. If you graph out maximum speed against grip, you'll find a nice curve where you can obtain your maximum speed either just before or just after the tires are at their complete limit. By going too far beyond the limit, the tires stop working, and the car slides excessively... this is classic "drifting." This is well outside of the range tires work best. Working the tires to one side or the other of the curve though can be equally effective, and will come down to driving style (though in the case of keeping it away from over-driving, it is often easier for a driver to "find more time" if under pressure since they have a little more leeway to play with). The next factor that comes into play is the balance of the vehicle and the specific course. While "drifting" does not gain anything, inducing oversteer to tighten a turn or widen your profile to both protect a line and straighten the exit is not the same. Given a the vehcile and tire combination that effectively worked at greater slip angles, you would be able to go through that same corner faster by keeping to just the fastest line and driving at the limit. But since there are always balance issues and tires work cannot work at all slip angles, sometimes the fastest route requires some creative throttle steering (similarly to issues you could find if driving on gravel or other surfaces where consitent traction becomes the issue to force some modification of "best approach"). It is almost always better to drive further to obtain a higher exit speed. If you break down most tracks, you'll find you spend about 50% of your time on a lap in corners, and about 50% on the straight... by driving 2 or 3 extra feet, you can gain a couple mph better exit speed, which is then maintained all the way down the next straight. Over an entire lap, this translates to massive differences in lap time (lose .05 in the corner, but gain .5 on the straight).