Everyone seems to be assuming that the V12 has more displacement than the V10.
If both engines have the same displacement, the V12 will breathe better and be able to rev higher (since the cylinders of a V12 are smaller for a given displacement than those of a V10, the pistons and connecting rods will be lighter, as will the valves, this means the mass will be more easily controlled and theoretical redline will be higher since there be less strain on the reciprocating components). The ability to rev higher and the better breathing will allow more top-end power, but will generally reduce low-end torque.
Now, the V12 will have slightly more internal friction, but overall the ability to rev higher will ultimately increase the power if all else is equal between the two engines.
You are correct that the V10 is cheaper (by virtue of having fewer parts), but it's actually slightly less efficient in terms of HP. Weight is up in the air because while the V10 has fewer pieces, the individual pieces of the V12, while more numerous, are also lighter on a per-piece basis. All else being equal, the V12 would probably weigh very slightly more, but I doubt it would be enough to really make much practical difference.
Yes! Finally. To elaborate on your "breathes better" remark, the reason is the total valve area can be much higher for a given displacement. Assuming the same bore is used, the valve area goes up by 20% for a given combustion chamber design. Using the same stroke, the valve area will be roughly the same, so there is no immediate drawback there (except maybe extra flow losses in the cylinder head, per cylinder.)
Another thing is that stroke-determined torque can be the same in comparable V10s and V12s, but the reciprocating mass per cylinder is still lower in the V12 (given the bore must be smaller to meet the same displacement) so the engine can still (potentially) rev higher. The better breathing could also improve mid-range torque, for the same stroke.
The biggest problem with V12s, especially at higher rpm (F1), is the internal friction - it robs power as to the square of the engine speed - because a V12 has a higher total bearing area and piston ring length than the equivalent V10. Longer camshafts can cause timing problems, too, as the shaft "winds up" - although that's less applicable to F1 these days. Straight sixes have tended to drive their cam shafts from the middle, rather than an end, to compensate. This obviously adds servicing complications.
A note on balance: V12s do have excellent balance - although all V engines have a rocking couple from side-to-side due to the cylinder offsets in the engine, and a slight "barrel roll" due to the bank angle. V10s have
another rocking couple inherited from the straight 5, which is end-to-end, like a three cylinder - hence the need for a balance shaft.
All engines have higher order vibrations due to the non-sinusoidal motion of the pistons and rods (crank and slider).
The three 120° crank offsets in a V12 produce a vibration at 6 times the crank frequency and at (2 / 10 000) times the magnitude of a single.
The five 144° offsets in the V10 crank (non-split pin) produces a vibration at ten times the crank frequency and at (7.5 / 10 000) times the magnitude of a single.
By comparison, a straight four has a vibration at twice the crank frequency and (4 / 10) times the magnitude of a single, so it is still very noticeable - hence the need for a balance shaft with higher displacements.
The magnitude comparisons are calculated for the same individual piston mass, i.e. the total piston mass increases with cylinder count and corresponds to engines with the same bore and stroke dimensions.
I'm not really seeing why this thread is actually in the GT5 section as opposed to our
Automotive section, so unless somebody can provide a valid reason, it will either be closed or moved over there...
All V12s are pretty badly reproduced, sonically, in GT5 whilst the V10s are fairly well represented in this regard - I can't think of much else, though.