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

House Ruler - Besides these karaka things, Sun & Venus 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-Venus Conjunction - So, this is one of the trickiest conjunctions one can have. First of all, they are natural enemies to each other as Sun represents Ego and Venus represents Relations and we all know that Ego & Relation can't go together. Its effects largely depend on degrees of Sun & Venus and how far they are from each other? If Sun and Venus are far away degree-wise then this shows that creativity & beauty of Venus is brightened by the light of Sun. This person can be very rich too. But problems come when Venus is coming closer and closer to Sun. Normally, it is said that Venus is combust within 6 degrees but in experience I have seen Venus giving results of combustion even when it is 20 degrees apart. So, we can say if Sun-Venus are together in a house then there is an effect of combustion,no matter how slightly. Now, what is the effect? Sun is karaka of Ego and Venus is karaka of Relationship. So, when these two are together than understand that Relations will suffer due to Ego Battles/Conflicts of couple involved. As Sun is stronger and fiery, Ego will win and Relationship will lose. As they get closer and closer degree-wise, person will experience more & more serious problems in relationship. Sun-Venus conjunction can be seen as one of the karaka of Divorce or Break-up. But this is about Jeeva Karaka. Regarding Ajeeva Karakas, this conjunction can be good as person can be extremely beautiful, charming and attractive as beauty of Venus is getting further brightness of Sun. Likewise, person can be highly creative with arts, media and movies etc as creativity of Venus is getting boost of Sun. Person can be extra rich too. But if Venus is combust then these traits will also suffer a bit and he has to put extra efforts to get results of creative pursuits and normally results will be seen in 30s. So overall, this conjunction is showing a lesson to person of letting go of Ego for keeping the relations alive. 

Who will win the Conjunction? - Sun will. Venus is just too mild and gentle to impact Sun in anyway possible. . 

Dignity & Strength - 

This conjunction will work best in Pisces, where Venus is exalted and Sun is in friendly sign. . 

In Aries, Gemini, Cancer, Leo, Virgo & Sagittarius, Sun will have full control over Venus as besides natural strength, it is also strong through dignity in these signs. 

Sun-Venus in Scorpio can be really troublesome for relations as Scorpio will add sudden ups/downs in relations after ego battles of Sun-Venus conjunction. 

In Taurus, Libra, Capricorn and Aquarius, Sun is weak. Hence, Venus will have some say here as it is in own sign or friendly sign. 

But overall, this conjunction is all about the battle between Ego and Relationship.