Which force is stronger: gravity or electromagnetism?
Unfortunately this question is like "if they had a fight, which would win: a lion or a shark?" It depends on the details. Like: are they fighting on land or in the water?
So, we should be more precise. Suppose you have two electrons. They repel due to electromagnetism - this is usually called the 'electrostatic' force - and they attract due to gravity. The electrostatic force between them is about 4.17 × 10⁴² times bigger than the gravitational force.
But suppose you have two protons. Their charge is just as big as that of the electron, with the opposite sign. But they are 1836 times as massive. So now we have to divide by 1836². The electrostatic force between protons is only 1.24 × 10³⁶ times bigger than the gravitational force. Still a lot, of course.
These statements are true for a wide range of distances. We could talk about what happens if the distance between the particles gets really small or really big, but very conservatively any distance between 10⁻¹⁰ meters and 10¹⁰ meters should be fine here.
Thanks to facts like this, people often say that electromagnetism is 10⁴⁰ times stronger than gravity. That's both vague and very rough, but it's easy to remember.
When you're dealing with stars, something very different happens. Their tends to be very small, per atom - precisely because electromagnetism is so strong that a highly charged star would explode! So the gravitational force between stars is vastly bigger than the electrostatic force between them.
And the same is true of other really big things, like planets or galaxies.
@robryk @johncarlosbaez why can't we have two neurons orbit each other under gravity alone?
@robryk - a proton is made of 2 quarks of charge 2/3 and one of charge -1/3, held together by the strong force.