The simplest way is to connect the two transformer outputs to an oscilloscope. A two channel scope triggered on one of the inputs would show the phase difference as the time difference between zero crossings. At 60 Hz, a one degree phase difference corresponds to a time difference of about 46 microseconds. If you put one signal on the vertical and one on the horizontal, you would get a Lissajous pattern from which the phase diffference can be calculated. A simple circuit would be an analog multiplier. The output of the multiplier is a sine wave at twice the input frequency and a DC value proportional to the sine of the phase difference between the two inputs. The 120 Hz signal can be filtered out by a low pass filter leaving only the DC term. For small phase differences (up to about 30 degrees) depending the required accuracy, the output DC will be directly proportional to the phase difference.