Usually aluminum frames of equivalent quality are slightly lighter weight. Not much, but you can measure the weight difference. Also today, due to economies of scale, aluminum frames are usually somewhat cheaper.
Sure, you could compare a butted thin-wall high-strength steel frame and the cheapest aluminum frame you can find that doesn't have butted tubes. In thus case, the steel frame could be even lighter. But that's not an apples-to-apples comparison.
The main benefits of steel are:
- Practically infinite fatigue life. If you subject an aluminum frame to a heavy load repeatedly, it will eventually break due to fatigue. Steel has a fatigue limit so if the load is below that limit, it will never fail.
- You don't have to worry about stripping threads. All threads in a frame have been designed for steel. When those same threads are reimplemented on aluminum, they are very weak and stripping is a major concern.
- The measurements of frames such as head tube size have been optimized for steel. Aluminum frames should optimally have larger head tube, which they usually don't (except today there are tapered tubes that have larger size where needed, specifically in the headset lower cup). Similarly for very heavy riders, cantilever brake post sizes might be a concern on aluminum forks.
- Ability to be cold set. If the rear hub over locknut dimension that is in fashion currently increases, you can bend a steel frame to the wider over locknut dimension.
- Repairability. If a steel frame fails, you can remove paint from a small area, weld it and repaint. Aluminum would require you to heat-treat, requiring stripping all components and paint, and then putting it to a heat treating oven that would destroy all components and paint if not removed, then refitting all components and repainting the entire frame.
I'd say if you expect a 30-year or longer life from your frame, get a steel frame, but do consider carefully what hub axle standards (thru-axle / QR, if thru-axle which from the many dozen competing standards), brake attachment standards (cantilever / one of many disc brake standards), bottom bracket standards (you should really get threaded BSA), seatpost standards (get the most common 27.2mm!), headset standards (you should really get external cup 28.6mm), rear over locknut dimension (130mm / 135mm) and eyelets (choose full for fenders, rear rack, front rack and headlight on fork crown) you get. Choosing unwisely can lead to a shorter than 30-year useful life. If you are happy about 10-year life, then aluminum is probably a better deal because aluminum frames are today more common, cheaper and lighter.
Also remember that on the low end of the market "steel" can mean gas pipe steel. Sometimes called "hi ten steel" where "hi ten" means "high-tensile" because there's a rumor someone could in theory build a bike from even weaker steel. Those gas pipe / hi-ten steel frames should be avoided at all costs, because they are practically never butted and also a lot of the steel is needed to make the bike durable which makes the bike very heavy. If buying a steel frame, the keyword to look for is the type of steel: it should be chromoly i.e. chromium molybdenum steel such as 4130, or a brand name steel like Reynolds, Columbus, Tange or Vitus.