Traditionally Mantra is recited and not written down. Likhita Japa is not mentioned in scriptures to my knowledge. But some modern day Gurus/saints do mention about the method's usefulness.
So, from scriptures, we can not know which method is the more efficient one.
Swami Sivananda, in his book "Japa Yoga - A COMPREHENSIVE TREATISE ON MANTRA-SASTRA", however mentions that writing down Mantras is very efficient among all the methods that we have:
14. Likhita Japa
Write down daily in a notebook your Ishta Mantra or Guru-Mantra, for
half an hour. When you write the Mantra, observe Mouna. Write the
Mantra clearly in ink. On Sundays and holidays, write this for one
hour. In a common place collect your friends also and let them write
the Mantras. This is Likhita Japa. you can develop a wonderful power
of concentration. Prescribe this to all of your family-members.
Incalculable spiritual benefits are derived from Likhita Japa
(Mantra-writing). Of the various methods of Japa described in the
scriptures, viz., Vaikhari, Upamsu and Manasika, etc., Likhita Japa is
very efficacious. It helps the Sadhaka in concentration of the mind
and gradually leads to meditation. An aspirant should select the
Mantra of his tutelary deity, or Ishta, according to his liking or
inclination. Repetition of the same Mantra with meaning and Bhava
should be practised both orally and in writing. For oral Japa, the
help of a Maala or rosary is required. For Likhita Japa a notebook and
a pen should be used. In Mantra-writing there is no restriction about
any particular script. It may be written in any language. The
following rules may be observed while practising Mantra-writing:-
- Regularity and punctuality of time should be observed. This would itself bring the requisite help and be of the utmost benefit to the
- Physical and mental purity should be observed. Before sitting for Mantra-writing, the face, hand and feet should be washed. Effort
should be made to keep the mind pure during Mantra-writing. Drive out
all worldly thoughts while writing Mantra.
- Continue to sit in one pose as long as possible. Frequent change of a pose or Asana should be avoided. Sitting in one Asana would increase
your power of endureance and also considerable energy will be
The notebook should be well kept and treated with respect and purity.
When completed, it should be stocked in a box and kept in your
meditation room in front of the Lord's picture. The very presence of
these Mantranotebooks will create favourable vibrations requisite for
your Sadhana. The benefits of Mantra-writing or Likhita Japa cannot
be adequately described. Besides bringing about purity of heart and
concentration of mind, Mantra-writing givesyou control of Asana,
control of Indriyas, particularly the sight and the tongue, and fills
you with the power of endurance. You attain peace of mind quickly. You
approach nearer to God through MantraSakti. These benefits can be
experienced only through regular and incessant practice of Likhita
Japa. Those who are not conversant with this Yoga should start the
practice immediately and even if they take to this practice for half
an hour daily, they will realise its benefits within six months.
(quotes are from page 87 onward of the PDF)
But, I don't think that we can prove this assertion from scriptures. That Likhita Japa is more efficient than the traditional method of chanting.