Growing and developing a strong local business model is a better path in my opinion. You could afford to make mistakes and learn quickly when you are at a stronger ground( a market you understand). When you're young, you'll lose your focus while thinking about the European market (using Europe as an example). European companies would ALWAYS (emphasis) spring up to cater to the European market. They might feel that they could cater the the local market better than a foreign organization and they might be right esp. if they have the focus.

Once, a startup has established itself in its focus market, grown and is ready to expand to another market, starting a branch in the European market becomes that much easier. The US success will certainly help in quickly establishing yourself as a global player.

Acquiring smaller companies in new markets is also a strategy that is quite successful and would be easier if you've succeeded in your local market. I'm pretty sure that Yelp would be able to acquire smaller European companies and use them as a starting point for a European expansion.

I'm not so sure first mover advantage really helps when moving to new markets since you are an early mover in your own market and are able to learn for this period there. Also, you could look at the strategy of existing players in new market to figure out the market differences. Because of this, I believe patience is a virtue when expanding to newer markets.