The saws were identical in size - 26 inch 5.5-6 point rip saws that are about 40 thousandths at the tooth line mid/back, and maybe slightly thinner at the to. Similar thickness at the top of the taper.
One saw was a disston 7, the other generic with no mark and a warranted superior medallion (but it was old enough to have a nib).
One never knows what steel was in them, it's a mistake to apply a "is it 1080 or 1095?" kind of thought to it. Most older saws were probably about 8 tents of a percent carbon, and hardened somewhere in the high 40s hardness range. You get the sense of the plate hardness by filing the teeth - both saws were new enough that the hardness was even toe to heel.
Just as another aside, every time I get an atkins crosscut saw, they are floppy compared to a disston. I would assume it's because of their tensioning process, because there is again, no difference under the file (and I think rob streeper on another forum actually struck these saws to confirm they're about the same hardness). Whatever it is that atkins did, it makes it so that if you want to convert a 7 or 8 point crosscut saw to rip for hardwoods or for resawing really hard woods, the saws don't have the stiffness to do the job without too much (in my opinion) care from the operator.
I suppose I have yet one more, a "tip top" marked rip saw that's actually a bit thicker than a comparable disston, but still floppier. Same with an old bakewell rip saw.
What you're lacking here isn't reading, it's getting out and filing and picking up some saws. You're not going to come to a reliable conclusion.
On a handsaw, the tension is in the surface. If you wanted to do an experiment for yourself, you could get a small but good quality panel saw (like an old disston 12 22-24 inch sized saw) and get a good stiff disston rip saw like a D8, and grind (by hand sanding) the D8 until it was similar thickness to the panel saw - about a hundreth less. If you did that by grinding off both sides, you'd be left with a floppy saw with no tension.
I haven't used a modern 1095 hand saw, but I have some doubts that they're as stiff as a good 1900 D8, even though you will have a whole lot of trouble finding someone who grinds as much off as disston did in tapering.