The 6 pr was more an infantry weapon, the 17 pr was a Royal Artillery piece. With APDS, the 6 pr was a very capable AT weapon and remained in British use for years.
I'm not saying the Jagdpanther was knocked out by a 6 pr..... Mind you, as the Panther series side armour is only 40mm (much the same as a Sherman), anything could have done it.
As for the similarities between 17 pr and 77mm, they do share the projectiles but that is all. The 77mm uses the WW1 3" 20 cwt AA shell cartriage which is a lot smaller than the 17 pr and the tube is shorter than the 17 pr as well. The balistic performance was not so different though. Both very good guns.