Not my flaired field of study, but one I pursued earlier in my college years, so I'll try.

They were widely popular in the context of their time. Comparing it to Michael Jackson would lead in the wrong direction, though, because

a) only relatively few people had access to concerts and the social levels to actually concern themselves with this form of higher culture and b) Media, in terms of those times, wasn't nearly as image-focused as it is today. Chances are that even those who admired Beethoven and Mozart in their times often had no real idea how they looked until they met them in person.

So, even more than today, we can't speak about the admiration of "the public" but of several "part-publics", which is really important to keep in mind. Those public parts who were able to follow higher culture were certainly aware of Mozart and Beethoven in their times and tried to socialize around them every now and then - either in Vienna or, when they were traveling, everywhere they came.

There's a nice anecdote about Beethoven - in 1812, he met with Johann Wolfgang von Goethe in Teplitz (Bohemia) - Goethe being the elderly master, Beethoven at 42 still relatively young. They took a walk through the park and people gathered, pointed fingers, were generally excited. Goethetold Beethoven that this kind of behaviour was really getting on his nerves, to which Beethoven replied "Your Honor [Hochwürden], don't be upset. It's possible that this is about me."

If you want to read more on Beethoven and his popularity at the times, there's a great book, unfortunately as far as I know only in dutch and german by Jan Caeyers: "Beethoven. Der einsame Revolutionär". It's a pretty long read but I sped through it in three or four days, as it's excellently written.

Mozart traveled, A LOT. Not just for the standards of his time, but for ours. I think we can safely say he spent close to a decade in his travels, and we are talking about a man who died at 35. He was in what we now call Germany, Austria, Switzerland, Italy, France, England, Belgium/the Netherlands, the Slovak and the Czech Republics. He visited quite a bunch of cities.

In modern times you see mega stars performing for the rich and powerful, at private events and also for public events. Well, in his travels, Mozart performed for super posh people in the big cities. At 15, he was commissioned to write an opera for the celebrations of the wedding of Archduke Ferdinand of Habsburg, in Milan.

These days mega stars make loads of money and live surrounded by glamour. Mozart made money by performing and being a piano teacher for the super rich, and later also made money by partnering with other people to present operas (this is new, in this period we start to see musicians become entrepreneurs. Before that, they were employees). He and his wife were into expending A LOT of money (there might have been some gambling, and he might have liked singers and actresses). It came to him asking pretty much everybody for large sums of money, and he would be using one loan to pay another (or at least some interest).

Mozart was a child prodigy. A lot of people were talking of the wonder boy. He was a well respected musician at a pretty young age.

His music circulated in different countries (as sheet music), and it was common for people to copy it (by hand). His sonatas and music for ensembles would be played at home, both by amateurs and hired professionals.

Beethoven traveled less than Mozart, but he visited several cities in Germany, Austria, Hungary, the Slovak and the Czech Republics. He spent most of his life in Vienna. He was working, and even living, close to the super rich. His music was known all over Europe and yes, it also managed to cross the Atlantic (there are surviving newspapers announcing concerts in which his music was played in the big Eastern cities of the US).

There were thousands of people at his funeral (10-30k), and it was published in newspapers in many cities (including the US).

So, were they Unknown dudes? Local celebrities? No, they weren't. They were way more well known than that. Michael Jackson mega stars? There was no such thing back in the day.

Mega stars are now known pretty much worldwide, by huge numbers of people. They are mostly known because of our modern means of communication. Tours certainly help, but not everybody who knows a mega star has been at one of their concerts. There is some personality cult for mega stars, their lifestyle is wanted by many and their lives become public. Their image and music are kind of a product for people to consume. It's a situation completely different from what Mozart/Beethoven lived.

The idea of "the idol artist" was kind of starting to be created. The first cases of anything similar to the modern personality cult I know would be Paganini and Liszt.