Suppose a foreigner, say someone from Singapore, wants to buy BHP Billiton which is listed on both U.S and Australian exchanges. Where should he buy BHP for maximum financial gain? Should it be buying from U.S exchange because brokerage cost in U.S is lower? What about differences in tax treatment with regards to dividends? Currency effects is to be ignored because it is too unpredictable.
It depends. An ADR might be exposed to a larger market (let's say American) with more volume and thus lower spreads, and thus cheaper. But it can also be the other way around, that the ADR serves a smaller market than the home market. I would go for the largest market, with the most volume so it's quicker and cheaper to buy/sell.
Often ADR has less shares, meaning that the availability is lower and the prices higher (more expensive). This is often the case with Asian stocks where governments try to limit their company's exposure to foreigners.
As a general rule I would buy the 'home' stock instead of ADR. From a tax standpoint it's also easier to comply with local laws. Your local accountant will be more familiar dealing with local stocks.
Both securities should have a high degree of correlation as the capital gain and income should be roughly the same.
Additional costs will come in the form of transaction fees, financing costs (if financed) and spreads, which will all take away from any gains that you make.
The market with the lowest spreads is generally the most liquid (the one with the highest volume or value traded).
Usually taxes on dividends have to be paid one way or the other. If the issuer of the dividend pays a tax on your behalf, you may in turn be able to claim that back when you file your taxes. The more foreign the stock is, the more work your accountant may need to do to correctly report your taxes, but shouldn't significantly affect your income. Your accountant and tax advisor should be able to clarify.