It really should be pretty much equivalent - arbitrage should keep the prices generally in synch.
There are a couple of differences - the spreads on thinly-traded ADRs could hurt when trading them (particularly true with a Japanese stock because the two exchanges aren't open at the same time). But you can also get screwed (to a lesser degree) by the FOREX spreads should your broker choose to do so. Finally, a sponsored ADR would protect you against a rights offering that isn't registered in the US.
Actually the f/x gain/loss may not hit the P&L but retained earnings depending on whether the sales are from off-shore subsidiaries and not repatriated versus export sales from the home parent company.