I just started a similar
thread and like others have spent a few quid on twitter apps that don't deliver. Currently trying twabbit and like it to a point but again like all the others they fail to have the consolidated Notifications pivot/column/hub of the official twitter app.
It makes sense (to me at least) to have all RT/*/New followers and conversations in one place, not have to hop (ha.. wabbit.. hop) about searching for them all.
When I get a notification in twabbit and if it's a fave of my tweet, I have no indication of it when I open the app. Frustrating.
Hopefully WP8.1 and the new 3 for 1 app development will bring other players to the phone.