What would be the difference in our strategie while optimizing for yahoo vs. google, are they both index a website on some similar matter or different?
No there strategy is something different. Like Yahoo give more importance domain age than Google, and some others.
Most of the time, the SEO strategies that you use for Google will work for Yahoo as well like creating optimized and relevant content, link building, on page SEO, and off page SEO.
difference is that with yahoo you wont see money with google you'll see lots of money so it's not that hard choosing between the two