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

Moon - Moon represents Mind, Emotions, Mother, Local Government, Peace of Mind, Home Environment, Water, Milk etc.

Venus - Venus is Beauty, Desire and Love, Liquid Money. Venus is the main significator of marriage. Venus represents girlfriend or wife for a man. Venus is the significator of all relations, may it be husband-wife or mother-daughter. Philosophically speaking, Venus is also the cause of all the sufferings in our life. How? Because Venus represents our desires and we get pain and suffering in our life only when our desires are not fulfilled.

House Ruler - Besides these karaka things, Moon & 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 Moon-Venus Conjunction - As much as it looks to be a beautiful conjunction as two of the most gentle and benefic planets are together, it may not turn-out to be so. The 1st reason is that Moon and Venus are mutual enemies to each other. There is a kind of planetary war going on between these two. Another reason is that Moon is Mind and Venus is Desires. So, person becomes desire oriented in life. It gives a me-first approach in all walks of life. As Venus represents relations too, mind becomes relationship focused. It means that person, with this conjunction, can't remain without relationship but this me-first approach then kicks-in and spoils the relation as relation is all about others, not self. Moon is Mother and Venus is Wife. So, if a Man has this conjunction then there is surely a chance of conflict between his Mother and his Wife. In that case, whichever planet is in better dignity, will have upper hand in conflict. At the same time, these people can be very beautiful and pleasant to talk with. They can be very good about dealing with Wealth & Financial Matters.They can be very creative and artistic too. It shows a special love towards Mother and Mother can be big source of wealth. They can love a very luxurious or 5-star living and if their partnet can't afford it, it can spoil the relationship. So, it looks a beautiful conjunction but actually requires lots of adjustment and compromises to do in relationship matters. 

Who will win the Conjunction? - Venus will. Person's mind will be totally occupied with Venus related things like Wealth, Finance, Luxury, Convenience and Relationship. These things bring peace of mind.

Dignity & Strength - 

This conjunction is best when Moon-Venus are in Taurus as it is own sign for Venus and exalted sign for Moon. Pisces is another good position as Venus is exalted and Moon is in friendly sign. It means that in these signs, person will be able to have reasonable desires with good cause.

In Aries, Cancer, Leo, & Sagittarius, Moon will have strength to decide which desires of Venus are reasonable and which are not as Moon is in stronger position than Venus in these signs. 

In Gemini, Virgo, Libra, Capricorn & Aquarius, Moon is in enemy signs. Hence, Venus will easily make mind go crazy with me-first approach. 

In Scorpio, it can be a tricky situation as always but if person spends time in research and occult matters, then this conjunction can lead person to gain a lot from Occult areas of life. Person can get into illegitimate, immoral or crazy relations in this position.