Currently, SpaceX has prices around 56-62 million USD per launch of a normal satellite (with a weight and orbit where they can recover the first stage).
Arianespace launches such lighter satellites in pairs, always two at once, at a price of around 60 million USD per satellite.
The Chinese launchers offer the same at around 70 million USD per launch.
So, the prices aren’t that different.
But, for launches from reused rockets, SpaceX is damn cheap. The first launch on a reused rocket cost below 30 million USD.
So, to recap: Today, in best case, SpaceX is between 4 and 13% cheaper than the next competitor. But in a few years, once they launch mostly reused rockets, they’ll be around 50 to 60% cheaper than the next competitor.
Long term, Musk is shooting for a ~100x reduction in launch costs to make a Mars colony feasible. Hope he makes it.