Difference between buying us stock on a us or eu exchange for european

Hi everyone,

Say I'm buying a s&p500 ETF from Europe. I can choose to buy it directly on a us stock exchange, or buy it on a local exchange.

If I buy it on a US exchange, I'll exchange euro for dollar on the purchase date and again when I sell. The same is true when I buy it on a local exchange.

Would my profits in both cases be identical? Is the only difference between the 2 which currency is used a base currency on the graphs?