The B44 is a great entry level pre '65 (oops sorry, it used to be). The pre'68 class is no longer on the cards either for National events. So the round or square barrel will both be eligible. The round barrel used to eb elibible for pre '65 and the square barrel for pre '70, but that changed with a commission ruling in 2005.
For an honest club racer these are great machines and with some heavy modification (all readily available mods) they can be made to go very well indeed.
Internally there is no difference between the round and square barrel motors. The round barrel just looks a little more "period". If the round barrel victors are allowed to race one day again in pre'65, then Firko's comments are valid. The difference between the GP engines and the standard EA engines was basically just the camshaft.
Put in an BSA B50MX grind camshaft, a good clutch, lengthen the swingarm to be the same length as the GP unit to make the bike handle like a GP, plus the usual goodies of good tyres and personal stuff and you'll have a ball.
Hope this helps.