Since you have just started here / you have time / you have done it until now / I don’t want to do it, why don’t you take responsibility for this project?

Or alternatively.

I have noticed you working on a past project, and I appreciate how you could keep things on track while still communicating well with everyone involved. This new project is important for us, to be able to better serve our customers and increase retention. I feel we have the best chances to succeed if you are going to take care of it.

Which one would make you feel more motivated to deliver your best possible work?

Which one is more often used from managers around the world?