Let's 1st understand what these planets represent on their own?

Sun - Sun represents Soul, Personality, King, Government, Father, Authority, Career, Top Positions, Ego, Self Esteem, Health, Education etc.

Ketu - Just like Rahu, Ketu also represents Illusion as both are illusionary planets but the difference is that Ketu is also the one who removes the illusion and brings enlightenment. Besides this, Ketu represents Isolation, Separation, Spirituality, Mystical World, Other Dimension means things related to Alien World, also represents Son, Dog, Intuition, Research Ability, Curious Nature, things which we have already achieved in past life and not much concerned to perform in this life. 

House Ruler - Besides these karaka things, Sun & Ketu will also rule some houses in your chart and will represent things related to that house. Of course we can't cover conjunctions Ascendant and house wise else it will never be over. So, you have to include those things at the time of interpreting this conjunction. Also, we need to keep in mind all Yogas and Raj-Yogas which their conjunction would be making to completely understand the conjunction. Here, we can only cover meaning as per karakas. 

Meaning of Sun-Ketu Conjunction - This is another position which gives an indication that person is born near Solar Eclipse. Again, closer the degrees of Ketu & Sun, closer the person is born to Solar Eclipse. It again gives all those results which were seen with Sun-Rahu conjunction but Rahu displays results outwards whereas Ketu leads it inwards. So, this person can be really introvert and may be thinking a lot about reason behind his lack of confidence. He may never express the same outwards. But the reason behind lack of Ego or Confidence is the same as it was with Sun-Rahu conjunction, i.e. Absence of Father. Ketu represents Separation and Sun is Father, so person may get separated from Father in early age. This causes lack of confidence or self-worth in his life. Even if, father is around, person can feel a mental separation from him as both sides are unable to understand each other point of view. Also, person may not have a clear idea about his Career or path in life as Sun is eclipsed and again success in Career delays up to 40s. From 40s only, person starts getting some authority in life. Or as Ketu represents Mysticism and Spirituality, it shows someone getting success in career related with mystical field. For such conjunctions of Sun with Rahu/Ketu, it is very necessary for Sun to be in good dignity to show some fight against these demons, else they will easily eclipse Sun and Sun's results till their maturity age. Also, in both cases, person may have some illusion, mis-information or confusion regarding his father which will be cleared only in 40s. 

Who will win the Conjunction? - Ketu matures at 48 years of age. Hence, till mid-40s at least, Ketu will certainly overpower or eclipse Sun. After mid-40s, it will be better for Sun. But if Sun is in good dignity like in Aries or Leo, then it will be battle of equals. Then Sun will withstand the eclipsing powers of Ketu and will have equal say in this conjunction. Else, it is all Ketu till mid-40s at least. 

Dignity & Strength - 

This conjunction will work best in Aries and Leo, as Sun will be in good strength. In all other signs, Ketu will easily grasp Sun till mid-40s at least.