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

Mercury - Mercury represents communication skills, marketing, calculative ability, younger siblings, hobbies, skills with hands, intelligence, quick decision making, logical thinking, youthfulness etc.

Saturn - It is all that which we don't like in our life. Saturn is Delay, Frustration, Restriction, Limitation and Anxiety. It is people of Authority, like Boss at your Work Place or Father-Figure at Home. Saturn is our Karmic Debt from past-life. Saturn is the things we didn't treat too well in our past life. Saturn is our Challenges and Lessons of life. Saturn is Old-Age, Teeth/Bones in Human Body, Diseases, Changes etc. Saturn represents our Step-Relations, it means that wherever Saturn sits, people related with that house give us Step Treatment. Saturn is Hard Work, Efforts and most importantly Perseverance etc. Nothing comes easy and in one go with Saturn. You have to work hard continuously over the longest possible period of life. Saturn makes a person Legend as Legends have one thing in common that they choose one field and work hard in it for whole life. 

House Ruler - Besides these karaka things, Mercury & Saturn 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 Mercury-Saturn Conjunction - 1st of all this conjunction shows someone who speaks or communicates very slowly. As Mercury is Communication and Saturn is slow in nature, they like to speak with certain slowness in their approach. They can also have certain delay in starting speaking in childhood and may be very introvert or fearful as Saturn will put a limit or fear on their communications. But whenever they speak, they speak with all seriousness and intent. At the same time, they can write lengthiest of articles and research work because energy will find its way to express itself anyhow. So, if they are not speaking much, then they will write at great length. As Saturn represents Law, they can be good counselors in Legal field. They can have very limited relation with their siblings. Although Saturn & Mercury are natural friends but such is the nature of Saturn that it is same for all. It doesn't discriminate. So, person can have real problems with his communication in early life and may have to work really hard at his communication to gain any benefit. At the same time, they can be very judicious or fair people as Mercury is Decision Making Skills and Saturn is the Lord of Justice. So, their opinions are never biased and they are able to keep themselves neutral. They can be good in learning Technical Languages or Ancient Languages. It can create a good editor. They both together also help in Business. But relations with siblings can be a challenge till mid 30s at least. 

Who will win the Conjunction? - Saturn will. Mercury is a neutral planet. It changes itself as per the planet it sits with. So, with Saturn, Mercury will change itself as per Saturn nature as discussed above. 

Dignity & Strength - 

This conjunction will work well, keeping in mind Saturn's nature of delay & hard work, in Taurus, Gemini, Virgo, Libra, Capricorn & Aquarius as both will be either in friendly/neutral/exalted signs. 

In Sagittarius & Pisces, person will be inclined towards Religious/Spiritual stuff but again, the understanding of any such stuff will be delayed till 30 years of age at least. 

In Cancer, this conjunction shows an emotionally repressed person. But this person can be good in writing emotional stories or nourishing/taking care of others as again the energy which is repressed will come out through one way or the other. 

It can be troublesome in Aries and Scorpio, but still can make a person good in Technical Languages.