We do not match 1:1 Pushbullet's features, we worked on our version from scratch (I'm pretty sure we both took advantage of the same APIs).
In our approach we focused on "pairing" devices with a simple/secure token, with no accounts needed (we do not require G+ account in order to register). We probably (still) address a subset of Pushbullet's features but still providing some other useful ones (as for our use cases) such as:
Phone "control", Device location, a simple Chrome Extension where you can keep track of your notifications (and interact with your Phone).
I'm pretty sure Pushbullet would do the same but we do not store any data and just "push" it between devices over secure channels.
Hope I gave you a more detailed view of what I meant.