From my experience older ‘traditional’ saws, even when freshly sharpened, will not cut as quickly as modern sabre / alligator style saws; the tooth pattern of these saws is ultra aggressive. I’ve crosscut a 2” board of hardwood by hand quicker than the same board was cut with a chainsaw at the woodyard (admittedly the chainsaw was somewhat dull). But once they are blunt they are destined for the trash as their hardened teeth can’t be filed (although they can be cut-up to make very good cabinet scrapers!).
I don’t believe you should expect to be getting results from dull, unset saws; it’s just not a fair test… sharpen them up and you’ll appreciated the difference. I find; if you’re used to powering through timber with a modern hand saw, you do have to tweak your technique to a more measured style to limiting buckling… Hope that helps.