There are pros and cons, but in most of the cases, I believe you should do it when launching your U.S. operations for at least three reasons.
First, because you want American prospective customers to feel at home when visiting your Web site. British English is different from American English mainly by the way people express an idea. American English is more straightforward with short sentences. It is usual for U.K. companies to spend money on translating brochures, user manuals and Web site into American English! Only non-English speaking countries believe that it is not worth the effort.

The second reason for building an American Web site is directly linked to your marketing and sales policy. At the start, you will not sell the same product line at the same price. You will probably focus on one or two of your products only. To get visibility and build a database of prospective customers in this new market, you may offer a freeware for example. Your user and server price policy will not be adapted for large deals and U.S. customer habits.

Finally, you may not want to boast that you are a European company: You came in the U.S. to do business, not to sell that you are a foreign-based company. By setting up a dedicated Web site to the U.S. market, you get the flexibility you need to adjust a marketing and sales policy for this market.