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

Jupiter - It is the most benefic planet and it represents all the auspicious things like Knowledge, Wisdom, Law, Guru, Spirituality, Religion, Philosophy, Literature, Elderly People and Children etc. For a girl, Jupiter also represents Husband.

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, Jupiter & 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 Jupiter-Saturn Conjunction - This can be seen as good/bad both conjunction. It all depends on patience and perseverance of person to know how good or bad this conjunction is going to act. 1st of all, these are 2 neutral planets together but Saturn will always have its say over other planet when it is conjunct, no matter which the other planet is. As Saturn delays things and Jupiter represents Knowledge & Education, this shows a situation where person's education can be blocked or delayed for some time. At the same time, person remains focused to complete his education anyhow. This person doesn't get good teachers in early life and he can have some real differences of opinion with them. They are the one who can ask any teacher or even Spiritual Guru as to whether they are sure if they are teaching the right knowledge. In short, right knowledge, right teacher and right Guru will be delayed in life. Likewise, right morals or belief system will develop late in life. Best example is Barack Obama with this conjunction in his 1st house who accepted that being a Drug Addict in early life was his biggest moral failure. So, this conjunction will delay all the Jupiter related things in life and person with discipline, focus, perseverance and patience will achieve those things only from 30s. So again, Saturn will play its role. In certain situations, this can create a fundamentalist who feels that only his beliefs or values are correct. Even right religious/spiritual views are developed from 30s. In early life, their teachers can be very harsh, strict or rude but in later life, they can get wise/old teachers. 

Who will win the Conjunction? - Saturn will. Jupiter will be impacted by Saturn's delay till 30 years of age at least. 

Dignity & Strength - 

This conjunction can work best in Capricorn. Although Jupiter is debilitated but it will get Neech Bhang Raaj Yoga from Saturn's presence. This will give success in Career but won't help much in personal life. 

In Sagittarius & Pisces also it can work well and person can be focused towards knowledge & education but in early life, person can have fundamentalist approach towards his religious and spiritual views.

In Taurus, Gemini, Virgo, Libra and Aquarius, Saturn will be strong. Hence, it will require person to put all the more efforts to get Jupiter related things. 

In Aries, Cancer, Leo & Scorpio, Jupiter will be strong. So, despite Jupiter's presence, if person goes through Jupiter MD, he can get right education at right time but still hard work will remain a factor.