The challenge in Europe begins on the university level. As an American who went to grad school in Europe (a technical university) - it was interesting to compare the differences.
It begins with the fact that at European universities, there's no real support for encouraging student entrepreneurship. In Sweden for example, they are making some headway with the Stockholm School of Entrepreneurship and other inititiatives (side bar: here's a great lecture with Niklas Zennström, off Skype and Andreas Ehn, former CTO of Spotify - http://www.youtube.com/watch?v=8R_E4GYfZK4)
There's a long way to go though!
Second is the cultural bias. If you are European (or have European friends) you will know that failure it treated quite differently in Europe vis-a-vis the USA.
In the USA, should you try a venture and fail, people say "well at least you tried!".
Or, you write about it in your grad school applications and get in. Then you have a fresh start.
Alternatively, you have a CV building experience. Often times, companies will look at your entrepreneurial zest favorably. Or, you can specifically apply to other startups who want people with startup experience.
Now, shall we compare that to the European experience?
European companies where you get the "evil eye" - at best you are looked upon with suspicion.
At worst, you don't even get considered.
The other issue is that many private universities in the USA are funded by wealthy business alumni. So there remains a strong relationship between industry and academia. The least of this is endowment money making its way to top VC's.
The last point is about cultural bias towards profit-seeking. In the USA, many socially conscious entrepreneurs see business and profits as a way not only to get wealthy, but to make the world a better place - create jobs, fund nonprofits, etc. The unhealthy notion that still exists in Europe (business owners are greedy capitalists that need to be bled dry), just won't work.
The best engineers and business dev/sales talent in Europe still seek out working for established companies. There's no "peer push" towards starting your own company. The elusive job security (which is quickly fading) is what people seek out.
Real entrepreneurs see owning a business as the secure option. Job employment and placing your future in someone else's hands seems insanely risky to us.
Family and friends deride the European entrepreneur who has this same mentality. This can affect relationships with loved ones and the like. Hell, even getting a mortgage or other normal activities is harder as a entrepreneur in Europe.
Of course, there's probably some hidden opportunity in these challenges as well. If anyone can think of any, I'd be curious to hear them.