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

Rahu - It represents Illusion, Foreign Lands, Foreign Things (foreign as in unknown things. So, for someone living in Punjab, culture and rituals of Kerala is also unknown and hence Foreign), Drugs, Medicines, any type of intoxication, Fame, Wealth, Success, Obsession, Past-life incomplete Desires, Movies, Television, Online World, Cheating, Imagined Fears, Unusual Things, Unique Things, Creativity, Rule breaker. Rahu also blows things out of proportions.

House Ruler - Besides these karaka things, Jupiter & Rahu 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-Rahu Conjunction - This is my most favorite conjunction on which I can talk as much as anyone wants me to. This is because it shows a person who questions everything. This conjunction creates a Guru Chandaal Yoga. The moment I saw this conjunction/yoga or Rahu-Jupiter mutual aspect in any chart, the 1st impression is always of a Rebel. This person will question every rule, regulation, ritual, principle and religion. This person can't be made to follow a set pattern. Gautama Buddha & Osho Rajneesh are best examples of this yoga. Actually, my inclination towards Osho Rajneesh, towards challenging/questioning every set pattern in Astrology and developing my own way of looking at chart also started when in 2015-16 Rahu-Jupiter got conjunct in Leo during transit and they were also transiting over my birth Rahu in Leo. So, this conjunction will always show someone who has the most weird views about Religion/God or any accepted Theory/Ritual/Principle. Give them a rule or philosophy and within few minutes they will screw every meaning of that philosophy. They will just prove to you that its all about how rich someone is with words and how he interprets same words in different meanings which is always possible. They can easily convert to any other religion or they can even create their own religion like Osho Rajneesh or Buddha. They are full of knowledge because Jupiter expands & Rahu explodes, so both together can explode person's knowledge beyond any limits. They will read about different religions and almost every possible readable thing in the world. They can be the most unusual type of Guru you can find. I don't see them working in jobs for long but even there they will have most unconventional ideas to make things work. They will have creative ideas to prosper their business. They can have huge wealth as Rahu is exploding the wealth of Jupiter. They can have fiery or courageous way of speaking. Spiritually, they will be seeker rather than believer. They won't believe in anything unless they experience it. So, in matters of God also, they want to know/experience God rather than merely believe in God. For them, "Belief" is a word without any foundation. So, when you see this conjunction, be ready for the most unusual discussion of your life. Also, the results of the house/sign they sit in can be exploded beyond imagination like, in Taurus/2nd house, person can be unimaginable wealthy, in Libra/7th house, he can be all about Relationship and can have many relations, likewise in Sagittarius/9th house, he can be all about gaining higher education & knowledge.

Who will win the Conjunction? - Rahu will. Jupiter is highly impacted by weirdness of Rahu. 

Dignity & Strength - 

This conjunction will be good wherever Jupiter is in good dignity because then Rahu will explode all the good results of Jupiter. So, this conjunction can be good in Aries, Cancer, Leo, Scorpio, Sagittarius and Pisces. 

In Taurus, person can be all about wealth and gaining wealth anyhow.

In Gemini & Virgo, person can be the smartest businessman and communicator. Person can be super analytical or super perfectionist. 

In Libra, as I said, all about relation and connecting with others. 

In Capricorn, a rebel against Govt or Law as he will have own approach of Law/Governance. In Aquarius, good gains from Large Organization or by following some higher purpose.