Good question with several answers that are contributing to what you are hearing. I am going to describe them in a list format because this subject comes up a lot and I get a number of PMs asking for more information, especially about WHY.
1. In general, power is power and when it's specified in the same units (ie. watts "RMS" which is the same as watts based on RMS voltage x RMS current), there's no difference. That said, there are some manufacturers that use different units, or do not specify the units, which can lead to great confusion. For clarification, there is also a unit of measurement in amplifiers called "peak power" which should be specified as watts (peak), which is generally 2x the RMS rated power. There is also a 20msec burst power which can vary by as much as 50% over the "continuous RMS" power. Combine the two and you can end up with peak burst power being as much as 4x the continuous RMS power. Continuous for the purpose of a bass guitar would be for a period of seconds rather than thousandths of a second.
2. Speakers in older combos and cabinets were much more often specified with less low frequency extension which allowed them to be higher sensitivity. Also, since they didn't have to handle as much power, the voice coil winding height didn't have to have as much overhang which also increased sensitivity. This certainly can explain a large amount of what you are experiencing, but at a significant sacrifice to the deeper low end extension and higher power handling that today's player seeks.
3. By limiting an amplifier's low frequency extension, this too can increase the effective efficiency. With many of the older, lower powered amps, the low frequency started rolling off between 40 and 70Hz which is not a bad compromise when you have limited power, and matches well with the typical speakers of the day. Since a bass guitar's lowest notes are more harmonics than fundamental, it's a passable compromise.
4. Today's (better quality) amps have much better low frequency extension, which takes more power to execute. Today's speakers also have better low frequency extension, which sounds "better" and more full, rich, round (insert adjective here) but this comes at a sacrifice to efficiency too.
So, yes, what you are experiencing makes sense, and this is WHY it makes sense.
Hope this helps