I am happy to answer to that question because I had the same doubts/questions.
1. the type of work is pretty the same, however I can say that strategy&, being part of the PWC network, focus more on the strategic part of a project and leave to PWC the implementation.
2. pretty the same but as far as I know stratgy& has smaller offices compared to Bain, thus they take care more at your personal life. In addition Startegy & does not have the up or out policy!
3. Prestige of course Bain, this is the reason why I decided Bain even though for the consultant position the salary is a little bit less.
4. Exit opportunities are very linked to the prestige, of course Bain is a stronger brand in your CV. But really depends on the clients you work with.