Transcendental Meditation creates a state of dynamic Silence.
Primordial Sound Meditation creates a state of static Silence.
The TM mantras are dynamic mantras, because they are derivations of Shakti mantras. Shakti is the principle of Movement and Vibration. Therefore you get a state of dynamic Silcence, which means that there are still prana flows going on while being in the Silent state. The Primordial Sound Meditation mantras are not Shakti mantras.
They are mantras which contain a seed sound (bija beej beeja mantra mantras) that is incorporated in a bigger mantra (Aum "seed mantra" namah. These sounds correspond to the position of the Moon in our horoscope athe the time of our birth. The Moon governs the Mind principle in our astrological chart (horoscope). Therefore, that specific sound that is associated with the specific position of the Moon at our time of birth, is also a sound which is very closely related to our Mind. Normally it is not possible to meditate with just the "seed sound", that is why "Aum" has been placed in front of it and "Namah" after it. Thus we get the Primordial Sound Mantra. Meditating with this mantra creates a faster and deeper Silence then the Silence with Transcendental Meditation. In Transcendental Meditation the effects are very much dependent of the way or the manner in which you meditate. In Primordial Sound Mediattion it doesn't matter : the mantra is so strong that by just thinking it, a sort of silence is produced that deepens during meditation and at times you wil just "be present" wtithout any thought or any breathing or anything at all. In this kind of meditation a part of the pranic currents in our body-mind system become silent, especially the pranic currents that cause the mind to be active. So the mind become inactive and you get a state of Static Silence (,because there occurs a stop or slowing down of the pranic currents that cause our mind to be active).
Both mediations are good to practice, because there is a slight difference between the states that are "achieved".
Both states are enjoyable. For example, you can practice the Transcendental Meditation in the morning and the Primordial Sound Meditation in the evening, or vice versa, dependent of what suites you.
Aum Gurudev Shree VishvaDevtAya Namah