It depends on where you live and what your dance goals are.
As the name implies, American style is danced mainly in the US. In other parts of the world, you will find few people who dance American style (though its popularity is growing in some areas).
In the US, American style is probably the most useful style for social dancing. It is what most people learn to begin with. So if your main goal is social dancing, you'll find more partners in most areas if you do American.
If you are interested in competing in the US, you can do either style. So the choice may depend on which style you like better and which teachers you choose to study with.
If you're not in the US, then I would recommend international. You'll have more opportunities in dancing with Int. in other countries.
If the two different lessons (and prices) are at different studios, I'd recommend checking out the studios before you decide. Get a sense of the atmosphere, costs, sales tactics, opportunities for competing, performing, and social dancing each offers, etc. You may find that you like one or the other more, and that might influence your decision.
Good luck! Whichever you choose, enjoy your dancing!