Recently, in the American Economic Review (here) Ignacio Palacios-Huerta, who published Soccernomics, and Jose Apesteguia analyzed 265 shootouts between 1970 and 2008. And one of the result, is that the team to kick first has a 60 percent chance of winning while the opponent that goes second wins 40 percent of shootouts. Note that this difference is significant
> prop.test(157,265)
 
	1-sample proportions test with continuity correction
 
data:  157 out of 265, null probability 0.5 
X-squared = 8.6943, df = 1, p-value = 0.003192
alternative hypothesis: true p is not equal to 0.5 
95 percent confidence interval:
 0.5304782 0.6517017 
sample estimates:
        p 
0.5924528
The study indicates that the advantage (ranging from 15 percent to 24 percent) exists across various types of competitions, international or domestic, neutral field or not and whether or not the first team is home or away. Further, note that the dataset can be downloaded here.