This is an interesting question. It looks to me like three-wheeled version is probably faster.
Your vehicle's top speed is set by the relation $P=Fv$, where $P$ is the maximum power available, $F$ is the total frictional force, and $v$ is the top speed. The frictional force has three contributions:
friction at the axles
Wind resistance probably isn't changed very much by a 3-wheel versus 4-wheel design, and friction at the axles is probably not as big as rolling resistance. Therefore let's focus on rolling resistance.
As described in more detail in my comment, you can't use the standard Amontons-Coulomb (AC) model of friction for rolling resistance. As far as I can tell from wikipedia, an appropriate relation for rolling resistance can be written in the form
$$ F_f=C(F_N)F_N, $$
where $F_f$ is the force of friction, $F_N$ is the normal force, and $C(F_N)$, unlike in the AC model, does depend at least somewhat on the normal force.
If $C$ were independent of $F_N$ as in the AC model, then it wouldn't matter how many wheels we had. Four wheels would give a certain amount of friction per wheel, which would be multiplied by four. Switching to three wheels would increase $F_N$ at each wheel, and therefore the friction per wheel, by a factor of 4/3, but this would only be multiplied by 3 wheels, so the effect would cancel out.
But $C$ does depend on $F_N$. The WP article has some information on how $C$ depends on $F_N$ for railroad cars and for pneumatic tires that have been optimally inflated for the load. The result appears to be that $C$ decreases with an increase in $F_N$. Therefore the result appears to be that the three-wheeled vehicle would be faster.
If fewer wheels give better efficiency, the question would be why we don't all ride around on unicycles.
For cars, I think four wheels are chosen for stability (and maybe handling?).
For train locomotives, the large number of wheels is so that the locomotive can be heavy (and get good traction) without damaging the tracks.