If you're going to resaw something wide, a frame saw is a better option if you're going to do it often, but not just any frame with any flimsy blade - rather something 3+ feet long (4 is better, and with enough thickness on the saw plate to be rigid under tension. Something like .04-.042" is commonly available.
otherwise, a coarse rip tooth saw will get you by.
the japanese saws with thin plates don't have enough plate stiffness to prevent wander, nor enough height - this is a no go for them. There are larger saws with thicker plates, but generally not in disposable types, and they won't do resawing as well as a frame saw.
As far as which is better, old or a new lynx? The old saws are better saws - nobody makes a carpenter's saw or a rip saw that's the equal of a disston #7 or D8 at this point. Steel, taper, tension, plate finish, handle, proportions - everything about the old saw is superior.
You are correct about buying a saw for resawing - it must be rip, and you must have it sharpened properly (which will be you doing it because it will like to be refreshed somewhat regularly). This is no place for combination saws or hard tooth saws- they are a crosscut tooth pattern, even when they claim to be "combination".
But to repeat, if you intend to do much resawing in the neighborhood of 12" wide, you'll find even a good carpenter's saw is a problem. if you do it once or twice a year, it'll be tiring because the saw plate just isn't long enough and you'll be banging the handle into the wood.
If you make a frame saw, the blade needs to be good and the proportions need to be right (don't be tempted to make one short or with a smaller blade or thinner - it'll be too short or it won't be stable or steerable in the cut). The saw itself doesn't, however, need to be high quality. I made a test saw years ago out of offcuts and screwed it together. The plate is tensioned with wedges that I just squeeze together with a clamp to set it, and the steel holding the plate is literally cheap soft mild steel that was cut from an old jointer drive belt guard. the idea was that if it worked well, I'd make a nice one with better parts, but it's never been necessary.
I did a good job on the saw plate, though, filed from 1095 spring steel that came in a roll. that part is important. I wouldn't make it much finer than 3 teeth per inch.
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Work with it is pleasant and easy. I don't tension it for narrower stuff like 4" wide boards or for sticking, but for something like guitar tops or bookmatching flat panels for doors, it's just dandy. to do 12" by 2 feet in oak would take about 15 minutes, and it's more accurate than my prior 18" band saw was (less wander in the cut) and can cut wider stock.
