Mozilla has conducted one of the first – maybe even the first – studies into the effectiveness of browser choice screens, and they conclude:
This research showed that browser choice screens have the potential to be effective. Well designed browser choice screens can improve competition, giving people meaningful choice and improving people’s satisfaction and feelings of control. And they can do all of this without overburdening people or taking too much of their time. What’s more, people have strong preferences: it turns out they want the ability to choose their default browser (rather than being assigned one by the operating system/device manufacturer); they also want to pick from a wider range of browsers.
You can download the full report from Mozilla.