I think that the International is basically the No.1A with the speciality stock, a light barrel, short and compact. Some like the full length wood, some don't, kinda an eye of the beholder type of thing. Somewhat chunky in weight for such a short rifle.
I think a poor barrel is a poor barrel, regardless of diameter/weight/length. Likewise, a good barrel is a good barrel, regardless of physical characteristics of weight, diameter, etc. Properly excuted, a barrelled action in a cradle will tend to show how the barrel will shoot on its own. Mann cradles have been used a long time for sorting barrels for match teams.
I do think that today's aftermarket barrels by the big makers are the top of the line, finely machined and destressed; usually very smooth inside and easy to clean properly broken in. Just a joy to own in my own opinion.
I believe that the more weight/size you have in a barrel the less the barrel is effected by outside sources, bedding, scope mount stresses, your hold, rest placements etc. However one has to fit the type of barrel to the style of use intended. The lighter barrel on average will be more sensitive to external pressures than a heavier one; but one still has to be able to carry it one might say. Obiviously a lot of parameters in what makes an accurate barrel and the influences it goes under in a rifle frame.
If a barrel is placed in a lathe, it is surprising how much deflection a barrel can move with just a lightest of touch; perhaps where the harmonics characteristics come into play in actual shooting. Some superlight barrels can be a trial to get to shoot, depends on your expectations of accuracy.