Pavane is right re cheapness. In particular it's the reason why Irish traditional players use the Anglo - they do it now because it's standard/traditional but the reason why they did in the first place was because Anglos were cheaper than English. Until I dicovered this recently I was puzzled about the use of the Anglo for Irish music because the English system seems obviously better.As for virtuosity on the Anglo, Noel Hill has been mentioned but John Kirkpatrick's playing demonstrates something the Anglo is surprisingly good at - playing chords and multi-part harmony. His first album Jump at the Sun incudes a solo performance of Mattheson's Gigue on Anglo conertina with no multitracking - and it's a four part fugue!
I've found recently that adapting an English concertina song accompaniment to Anglo results in a totally different sound - the same basic harmony but with the notes of the chords or countermelodies in quite different places. Neither instrument can easily do exactly what the other can.
Anahata
PS Shameless plug - my own arrangement of a duet concertina tune for Anglo is in this HERE
Challenge: try that on an English!)