If you're looking at this through the lens of which index fund to choose then there are a few additional things to consider:
1) Currency exchange rates. Is the index fund sold in your home country's currency? -- In Canada VUN and VTI both track the US stock market, but one is sold in Canadian Dollars and the other in US dollars. What does your bank charge for currency exchange?
2) Foreign withholding tax. Dividends paid to you through a fund that exists in another country may be subject to foreign withholding taxes. These can sometimes be circumvented/recovered by keeping the fund in a tax free retirement savings account, but it will depend on the tax law that exists between your respective countries.
3) Consider time scales and time lines-- it's fine to look at two indexes and see that the SX5E has outperformed the S&P recently, but what about over a 5 year period or 5 years ago? You'll be able to find some areas that one beat the other at some point. Past performance isn't a guarantee of future gain. That said I like the US total stock market's track record.
4) There's always the world index if you want to further hedge your bet. Though this tends to be swayed a lot by the US stock market. Though this may not always be the case.
5) There's an emotional argument you can make for investing in your own country's stock market in the sense that you're betting on the continued growth and success of your nation's economy, but I'm not sure it necessarily makes financial sense.
6) Management expense ratios. Just because they're both tracking an index doesn't mean that they're both equally cheap to manage.