Tubing diameter will also play a roll. The thicker the tubing the thinner the walls can be, for a lighter frame that is still stiff and responsive.
As other have said, I also think geo is very important and you'll want to get a bike with geo that matches the type of riding you want to do. For example 2 of my steels, both lugged, one with tange prestige tubing and one with larger diameter true temper OXII tubing are both quality steel frames, but ride very differently not so much because of the difference in steel, but mainly because of the geo.
My MB1 with Tange Prestige is built for more XC type trails, fast, compliant and very comfortable, but is not so good when the trail gets rough, on tight twisty trails or for bunny hoping and jumping. My singletrack with True Temper OXII is built for aggressive trail riding, very responsive, stiff, quick and easy to maneuver and a blast to jump and hop, but not as good on climbs, long stretches keeping speed or xc type rides where you want to be in a less aggressive riding position.
Another very important thing you may want to consider is how big of a tire you can fit on the frame. Frames from the 80's, like my MB1 often can't fit much more than a 2" tire, while my singletrack can easily fit a high volume 2.5" tire and can even fit a 27.5" in the rear (need a different fork to fit 27.5" in the front). For XC type riding the skinnier light tire works great, but for rough trail riding, fast cornering and jumping the high volume tire is a huge improvement in performance and can be run with much lower PSI for better traction and shock absorption. The high volume tire also provides about an 1' increase in diameter and runs just over 27", while the 2" wide tire is more of a true 26".
If your looking to convert an older steel frame into more of a modern rider, then the tire size the bike can fit might be something to consider since running high volume tires are one of the big advantages of modern frames.