Bring it. I cannot stress this enough. We brought it all... crib, stroller, changing table, clothes, etc... We also came over when my wife was pregnant (7 months at the time of move), and it was the best idea by far for the following reasons:

-Price: Those $3 onesies at Target? Try 30-40 CHF here. Everything else is wildly more expensive here.
-Time constraints... shops close very early, and you will simply not have the time to handle the move along with shopping for all the baby stuff. The move while being pregnant is stressful enough, so best not to add more to it.
-The company paid for the move, so why not? ;-) The container was a fixed price with or without baby stuff.

I argued with my wife at the time that it was not necessary to buy everything in the US, but she won that argument, and of course she was right.

We now have the apartment ready and nothing to do but wait for baby... due Dec. 31.

Oh, and bring maternity clothes too. My wife found lots of cute boutique maternity stores, but a pair of maternity jeans averages around 300+ CHF.

Good luck!

-Alan-