Sri Vaishnavas believe there are two paths to Moksha, Bhakti Yoga and Sharanagati (aka Prapatti). Bhakti Yoga is a long and difficult path to Moksha, and it has both Karma Yoga and Jnana Yoga as Angas. Here is how Vedanta Desikan describes this path in the Rahasyatraya Sara:
Karma Yoga means the performance of certain kinds of Karmas or rites and duties as the result of knowledge acquired from the shastras in regard to the true nature of the Jivatma and the Paramatma. The rites and duties consist of the following: (1) Nitya Karmas or regular duties to be performed compulsorily (2) Naimittika Karma or rites to be performed compulsorily on special occasions (3) such Kamya Karma or rites as are optional and as have been chosen to be within one's ability.... Though these Kamya rites are ordained for obtaining specified fruits like Svarga, they have to be performed without any desire for those fruits.... Karma Yoga, either through Jnana Yoga or without it, becomes the means of having a vision of one's own self or soul, with the help of Yogic auxiliaries like Yama, Niyama, and Pranayama.
Jnana Yoga is the constant and uninterrupted contemplation, by one who has conquered his mind by Karma Yoga, of his Svarupa or essential nature or the self as being distinct from matter - his Svarupa which is the mode or Prakara of Ishwara in virtue of its relation to Him as his body or Sharira.... If a person has succeeded in obtaining a vision of his self by the practice of Yoga preceded by Karma Yoga and Jnana Yoga and if he escapes the snare of being attracted by the pleasure of enjoying this vision which is so great as to create a distaste for all sense-pleasures - then he begins the practice of Bhakti Yoga, which is the means for the attainment of the supreme goal of enjoying Bhagavan.
Bhakti Yoga is the special form of meditation which is of the form of unsurpassed love and which has, for its object, the essential nature and the like of Bhagwan who is not dependent on anyone else, who is not subject to the authority of anyone else and who does not exist for the fulfillment of the purpose of anyone else. Bhakti is of the form of a continuous stream of knowledge which is of the nature of uninterrupted memory like oil streaming down continuously; it has clearness similar to that of visual perception; it grows from strength to strength by being practiced every day until the day of journey to Paramapada and terminates in the remembrance [of Vishnu] of the last moment. The performance of the rites and duties of one's Varna and Ashrama is auxiliary to it, as it dispels sins that cause Rajas and Tamas which, like weeds, impede the growth of Sattvam so necessary for the expansion of knowledge.... Bhakti Yoga which has thus been prescribed as the means of obtaining Moksha has been called Parabhakti. It produces in its turn an eager desire and determination to see the Lord[.]... By this keen desire alone, he wins the grace of Bhagavan who awards him with a perfect visual perception of himself for the time being. This visual perception is called Parajnana. From this perfect vision of the Svarupa of the Lord is born an excessive an unsurpassed love for the Lord similar to that felt by a man suffering from great thirst at the sight of a tank. This is called Paramabhakti. Paramabhakti produces an eager desire and determination to enjoy the Lord without any limitations, as the Bhakti feels that it is impossible to live any longer without the experience of the Lord[.]... It causes an excessive eagerness in the Lord to give him Moksha immediately and makes him attain Moksha after quenching his great thirst for union.
Whew! In any case, Sharanagati is a much easier alternative to all that; you just surrender to the lotus feet of Sriman Narayana and then you'll attain Moksha as soon as you die. (You can see the ritual needed to surrender here.) Here is how Vedanta Desikan describes the advantages over Sharanagati over Bhakti Yoga:
[He who pursues Bhakti Yoga] is capable, like Vyasa and others, of other means or Upayas than Prapatti and is therefore not absolutely helpless. Since he can bear delay, he is not averse to other interest. He will attain Moksha only at the expiration of the Karma which has already begun to yield fruit, when he will have the intense thought of the last moment before death. Since the primary Upaya or means which he has chosen is Upasana or Bhakti, he attains the fruit thereof, namely, Moksha, when it is performed fully and in accordance with the rules and injunctions prescribed for it. On the other hand, Prapatti adopted as the primary or direct means is open to all Adhikaris, is capable of averting all hindrances, can further the attainment of all that is desired, is easy of performance, has to be performed only once, can bring about the fulfillment quickly and will not countenance any opposition or obstacle.... The man who has resorted to Prapatti as the direct and independent means will have no hindrances at all in the way of his attaining the perfect enjoyment. Therefore from the moment of the performance of Prapatti, there is nothing in the way of his attaining Moksha but his own desire to live till the death of this body so that he may enjoy such things as the rendering of service with this body to the images of the Lord to which he has an attachment. So his Moksha has to await only the death of this body and will consist in rendering, in Vaikuntha, or perfect and full service which has begun even here in the performance of service limited by the conditions of place, time and the nature of bodily life.
Let me close by explaining one other comparison Vedanta Desikan makes between Bhakti Yoga and Sharanagati:
Among those who resort to the Dharmas of renunciation as a means for the attainment of the supreme goal of life, there are two classes of qualified persons: those who adopt Prapatti as the sole and direct means and those to whom Prapatti is auxiliary to the chief means, viz., Bhakti. Both these are Prapannas, one adopting Prapatti as an independent means and the other adopting it as Anga to Bhakti. both of them are also called Bhaktas, because Bhakti is the Phala or fruit for one and Sadhana or means for the other.
This is a profound statement, so it's worth explaining in detail. For one who does Bhakti Yoga, Sharanagati is an Anga and Bhakti is the means. Bhakti Yoga involves meditating upon Brahman using the 32 Brahmavidyas found in various Upanishads. One of these is the Nyasa Vidya, which 8/ about Sharanagati. Now you may be wondering, if Bhakti Yogi and Sharanagati are two different paths to Moksha, then how can one of the Brahmavidyas meditated upon in Bhakti Yoga be about Sharanagati? The answer is that there are (at least) two kinds of Sharanagati. There is regular Sharanagati, where you completely surrender to Sriman Narayana and get rid of your entire stock of Sanchita Karma so that you'll attain Moksha. And then there is Anga Prapatti, a more limited form of surrender which people do as an aid to Bhakti Yoga where they just clear the narrow set of sins that stand as an obstacle to Bhakti Yoga. Ramanujacharya discusses this in his Bhagavad Gita Bhashya. In any case, Bhakti or devotion to Sriman Narayana is the means by which someone who pursues Bhakti Yoga attains Moksha.
Conversely, for one who performs Sharanagati, Sharanagati is the means and Bhakti is a fruit. That is, Sharanagati is the means by which you attain Moksha. And Bhakti is a fruit, because after you surrender to him, Sriman Narayana gradually fills your heart with such love for him that you'll eventually become a great devotee of his, even if you didn't have much devotion beforehand.
