Hi scoosh, do a search and you'll find a lot of debates on this one!
2 things... there are a lot of generalisations, and secondly... it depends.
The feel of a bike-frame is a blend of materials used, geometry and jointing method. Al materials have a blend of strength/rigidity to weight as well as resistance to constant flexing/vibration i.e fatigue. Then add that there are different types of steel and sifferent types of Aluminium you can understan that there are lots of combinations and permutations. There are a few materials science bods around that can give the detail.... Suffice to say that all bike frames are built differently and whilst there are some sweeping genaralisations, not all of them are strictly true in all cases...
The generalisations are things like, Steel is flexy and comfortable, Steel flexes so is not as efficient as a stiffer material say aluminium, so not as fast,
Aluminium frames are stiff and harsh...
Well...
I have an old Reynolds 531 tubed steel Holdsworth, circa 1949, plain tubes, pencil thin stays, really curved fork. When pedalling hard you can see the bottom-bracket move visibly sideways, in fact it flexes so much that you can make the rear tyre rub the chainstay. It's a magic carpet of a bike, more comfortable than your fave sofa AND footstool.
I also have a Reynolds 531 tubed steel MTB, circa 1985 ish, big curvey forks, very relaxed head and seat angles riding on big fat tyres... and it'll shake your fillings out on a rough-surfaced road.
I had a mid 90's Omegar race-bike with classic angles, straight forks Columbus Nivachrome steel, top racing stuff, bottom bracket barely moved when putting the power down, felt every grain of grit on the road, but it also had a certain springiness to it.
I have a 2004 Aluminium 6061 compact framed Giant TCR1, large diameter hydroformed tubes no bottom bracket flex at all fairly up right angles, straight (carbon) forks... smoother than a babies bottom, responsive, glides over rough surfaces... magic. My mates cruder aluminium hybrid feels very responsive but also feels like it's trying to shake you to death.
So, only from experience, steel can be soft and squidgy lovelyness or a bone-breaker, aluminium can be a magic carpet. The Guru Sheldon Brown also reckons that the bottom-bracket flex on some bikes does not render them less efficient in terms of power transfer... but I can't find that paper right now.
So, to specifics...
Steel tube grades can easily be made into frames that are by character a "springier" than Aluminium. This character of steel (and also Titanium) makes it very suitable for long-distance riding where comfort is highly valued. Steel frames are also very strong in a way that makes them suitable for hauling loads too (though there are aluminium touring and trekking bikes the majority are steel). Also... steel can be fixed pretty much anywhere in the world, Aluminium cannot. Steel also fails less catastrophically than aluminium and carbon.
Handling and comfort are not mutually exclusive a bike can still have a sharp handling ride but have good vibe absorbing properties.
Steel bikes with very little TLC will last donkeys years.
Steel bikes may on balance be slighty heavier but not much... by the time you've addad tools, water mudguards etc, the difference becomes increasingly inconsequential.