Premium Mustang's live rear axle causes the inside wheel to lose grip from heavy tire deformation due to the angle of the axle to the ground. This causes the outside wheel to spin the car out easily under power. The Cobra has fully independent rear suspension, and does not suffer from this problem. It is likely that your heavy understeer setting is forcing you to use the throttle to drift more than usual, and this effect is amplified. To counteract this, using a slightly higher rear camber than your body roll angle is ideal. The number entirely depends on how much roll the car is facing, which depends on your suspension settings and the tire's grip.
If you are getting oversteer from drifting without power, then it could be the body roll. If your springs are too loose for the drop amount and weight over each wheel for a given G level, the outside wheels could be bottoming out, enhancing the previous effect by causing harmonic motion that bounces the inside wheel upward (from bouncing the bottoming-out-body on the outside wheel, since they are linked by a single axle) adding to the effect. If you are a relatively new drifter, your driving style will probably feature sharp changes in G forces that can easily cause this.
Outside of this, driving style will affect this greater. It could be that your second moment of inertia, as well as your steering ratios, are poor enough that the delay between steering input and reaction in the car (especially if the front wheels are not receiving enough weight to have enough grip to speed up the turn-in process), then you should start the drift earlier before the corner and take a wider line with less angle. You will slow down relative cornering time to your angle (and thus might fall behind a leading car of equivalent speed), but it's a lot faster than crashing.
Also, keep in mind that peak power means nothing in a drift car. It has to do with the average spread of torque at the engine multiplied by the various gear ratios (including the tire diameter) and its relative measure against the grip coefficient of the tires. Another thing to worry about is the -shape- of your power. Using the Horsepower and Torque graph in the tuning sheet, look for the RPMs where the torque rises and falls. If you apply throttle to rising RPMs in the middle of a drift, it is possible to get a sudden "surge" of power that overwhelms the tires, and while a fast drifter can compensate for this, can make the car wildly unpredictable to someone with a slower reaction time or less knowledge of how their car handles.