If it's the same company and the same class of shares, it doesn't make any difference (in terms of performance and dividends) which country and which currency you choose.
I understand you are not based in the US, but because one of the alternatives you stated is the US you may find it useful to read the International Investing brochure by the SEC. Make sure you understand the difference between directly listed foreign companies and ADRs. The latter are actually much more common, are structured a bit differently and may come with extra fees. The trading and the ultimate economic effect is not very different though.
If your base currency is none of the two currencies, it is best to buy the stock in the market that is more liquid and has lower transaction costs - which is usually the country where the company is based and/or where it was listed first, but not always (especially when the other country is US).
Consider average trading volume, commissions, and the bid-ask spread - not only in the stock itself, but also in the currency. Another thing to check are possible differences in regulatory and tax implications, which could make one country more favourable than the other in your particular situation.
In general, the price (converted to your base currency) should be the same on both exchanges, although occasional temporary mispricings may occur, especially when one of the markets is illiquid. These mispricings can sometimes be exploited by arbitrage, although that is usually inaccessible to a retail investor due to high transaction costs. I did this kind of arbitrage a few times as part of my previous job, but the opportunities were rare and profits very small - usually the prices matched closely. The mere possibility that arbitrage could be done is actually the reason why the price is the same in both places.
This also means that currency risk is not a factor when comparing the two options, because relative changes in stock prices and currency exchange rates will always offset each other, and in your base currency the performance will be the same.