It's a characteristic that Broad's shown mainly in ODi cricket, he very rarely dismisses tail-enders, and more often than not dismisses the top-order batsmen, and it appears he's starting to convert that into Test cricket. Here are the full list of his ODi wickets, excluding a few against Ireland iirc:
How
Yuvraj
Bravo
Gibbs
Sangakkara
Silva
McCullum
Styris
Taylor
Gayle
Ramdin
Botha
Karthik
Raina
Ryder
Sehwag
Smith
Dhoni
Mills
Chanderpaul
Tendulkar
Ganguly
Gambhir
Oram
Powar
Sarwan
Razzaq
Agarkar
Duminy
Jayawardene
Fernando
Kallis
Akmal
Mubarak
Sammy
Vaas
Younis Khan
Samuels
R Sharma
Akhtar
Malik
Tharanga
G Smith
The bolded guys are the lower-order bowlers and they're very few and far between. That's a list of some very good international batsmen right there, and if he can get that Test average down to the same sort of region as his ODi average, then he'll have done very well. I can see no reason why he can't, he doesn't seem to be the typical England player that's happy to settle for mediocrity. The talk in the England camp is that he's improving and learning every day, and that's finally starting to show in both forms of the game. With Anderson and Broad both starting to find some real form, things have to be looking on the up for England, could have a very, very good attack in a year or so if Onions continues to develop.