Personally, I don't think I'll use it - I use dropbox when I want to sync a file with my phone, Evernote for notes and lists, and just Chrome to Phone for addresses (via google maps) or urls.
I want to be able to put my own notes, lists, etc on my phone, not just webpages and links. And files too, of course.
Simply, PushBullet will be a superset of Chrome to Phone.
A big annoyance of mine with CtP is it's one-way, I can't send links to a browser. Would it be possible to PushBullet a file/link back to a browser? Maybe the last browser that pushed to the phone?