I was wondering about what are the advantages/disadvantages of trading US stocks on the American Stock Exchange from a non US broker versus trading the same US stocks on a non US stock exchange from a non US broker both in the same country?
In some cases the stock is more liquid on its home exchange, meaning you can benefit from a smaller bid/ask spread. (How much this can matter is limited though, because if the prices between two exchanged get more than minimally out of sync, arbitrageurs will jump in and buy stock on one exchange to sell on the other until the imbalance has disappeared).
On the other hand, if the cash you have on hand to buy the stock for is not USD, then you'll generally be at the mercy of the exchange rates your broker offers after you have traded. (Or alternatively you would need to transfer your money into an USD account in advance, before you know the exact amount you will need for your trade). If the stock happens to be listed on another exchange where trades settle in your currency, the exchange rate cost/risk associated with the trade itself disappears: you will know exactly what a bid will cost you when you make it.
Of course the broker may charge different fees for trades on the two exchanges too, but this varies between brokers anyway, so it's hard to say anything general about.