I read on the Internet that "many" is formal and "a lot of" is informal, but in certain sentences, I prefer to use one of these regardless of their level of formality. For example, when they come at the beginning of the sentence, I tend to use "a lot of", as in:
A lot of tourists visit my country.
I wonder if the alternative sentence, i.e.: "Many tourists visit my country" sounds just as good to a native speaker. I could be wrong, but "a lot of" seems to be more emphatic than "many" and I get the feeling that "a lot of" refers to a much greater number than "many". Does my feeling have any ground in reality or do the two mean exactly the same?
How do native speakers choose between the two? Are the two always interchangable when used with countable nouns?