Investing in European companies stocks from US vs. from Europe

Let's say that I have some amount of cache to invest and I want to do so on companies that have their business primarily in Europe and can also be traded on the US stock market (e.g. Novo-Nordisk \[NVO\]).

Let's also say that you have dual citizenship and you can decide to trade that stock either in the US market, or you can open a broker account in a country in Europe, move US dollars there (and convert them to euros in the process) and trade the same stock there.

Which option would be the best (and why)?

* trading in the US (e.g. Fidelity)
* trading it in Europe

thanks!