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

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. 

Ketu - Just like Rahu, Ketu also represents Illusion as both are ilusionary 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, Saturn & 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 Saturn-Ketu Conjunction - So, this is another stressful combination you can have where things related to the house where it falls will be severely impacted, like in 4th house the relation with mother and home environment or in 5th house the relation with children or the love interests. Again, two strong malefics are together making you work really hard. As Ketu represents isolation & separation and Saturn is our duties & commitments in life, these people constantly feel separated from the work they are doing, especially if it is a routine job setup work. They remain a seeker of their real duties in this life as they feel isolated from a normal routine work. As Saturn represents Law & Govt, they can go into legal field but on personal level they may not be very law abiding or principled people themselves. That's why, they don't like routine jobs or following a routine way of living. In the end, they can find peace in unusual fields like Occult or Spirituality as Ketu represents these things and Saturn is our duties in life. 

Also, Ketu represents things which we have already achieved in past-life but if a planet is conjunct Ketu that means person still have some issues pending with things related with that planet. As Saturn represents duties, this is why these people come in this life to search their right duty in this world. Saturn would also rule two houses in their charts through its signs Capricorn & Aquarius and people will have some left-over karma with things related with that house. 

The difference between Saturn-Rahu & Saturn-Ketu conjunction is of Exploding & Imploding. Struggle of Saturn-Rahu conjunction is very much visible to others as Rahu explodes the delays, hard work, struggles and perseverance. But with Saturn-Ketu conjunction, person would internally think, assess, re-assess and create a huge mess within himself. Emotionally, both these conjunctions can be very draining. This conjunction can make someone very good at research work. 

Who will win the Conjunction? - Saturn will, at any day. 

Dignity & Strength - 

Just like Saturn-Rahu, this conjunction is also same in all signs and houses. 

Sometimes I feel that malefic planets should be karaka of Equality, lol. They are same for everyone & anyone and in whichever position/dignity. They never discriminate.