Andrew said “that both of the backsaws are 1970 or later.  Is it worth
attempting to sharpen them or should I keep an eye out for older saws?
What makes an older saw better?  Is it that the steel is better quality so
the teeth take  and hold a better edge?  “

Do you own a pair of calipers, or maybe a 0-1” micrometer?  Measure the
thickness of the steel at the heel and the toe just above the teeth along
the cutting edge, and also along the backside, furthest away from the
teeth.  The best quality saws were taper ground, so that the saw plate was
thickest at the heel along the tooth line, and gently tapering to thinner
steel at the tip and the back.  Modern makers use 1095 spring steel
(basically the same blue steel bands used to band lumber together at box
stores).  Older makers used to also “tension” the steel along the tooth
line by hammering the metal to cause internal stresses to cause it to want
to stay straight.
    Backsaws are different- the saw plate is of uniform thickness, and the
spine pinches the plate and tensions the cutting side (so you can gently
tap the back on the bench if the plate is a bit wavy along the tooth line
to retension it- of course it’s obvious this doesn’t work on newfangled
saws with milled slots with plates that are epoxied in place- this only
applies to rolled steel or rolled brass back saws that only pinch the
plate).  Smaller 6”dovetail backsaws had thinner plates maybe 15 thou, and
large tenon saws up to 40 or 50 thou or so.

To answer to your question, you have to remember that manufacturers made
cheap crap in the old days also, and just because it’s old doesn’t mean
it’s good, and vice versa- just because it’s recent vintage doesn’t mean
it’s crap either.  There were good tools made all over the place, just as
there were cheap tools made for occasional use- stuff made to a price
point.
  I would recommend that you definitely sharpen up the ones you already
have, and use them.  First, as an exercise (it takes practice to learn how
to do anything- you can only practice by doing, not reading about it or
watching videos- you actually have to do it).  It will teach you how hard
the steel is, and you can learn about tooth geometry and set and so on, and
the performance will help you learn to appreciate what “good” means when
you get a really good saw in your hands.
As for bent blades, fixing these takes a lot of experience, and although
I’ve tried to fix some, I’ve only had the occasional success- usually I
leave the bent saws for someone else. A slight bend you may relax by gently
curving the blade over (and old book mentions that you should be able to
bring the toe to the handle!) but only you can judge if it’s useable or
not.   In the olden days, there was always a ‘sawsmith’ in building camps
and lumber camps.  It was a skill set that took years of practice and
learning, don’t kid yourself into thinking you can figure it all out on
your own by watching a few videos and reading old books in a couple of
afternoons.  Manual skills require manual exercises, so definitely start
practicing, but don’t necessarily expect success right off the bat.
 (Otherwise we could have all sorts of basement dentistry and home surgery
clinics all over the place, right?)
Cheers from Waterloo
Claudio