I think comparing old desktop with new laptop is going to give you different experience than comparing old laptop with new laptop.
I got M1 Air and not only is it a huge difference from my previous 2017 MPB 13" (which I gave to my mother who spilled coffee into her previous laptop), it is much better than my work provided 2019 MBP 16".
"Snappiness" is subjective and hard to measure, but the thermals are huge difference. My work MBP is sitting at 63°C with just Firefox pointed at HN. On both my old MBP and the work one, playing 1440p video (native screen resolution) would make it loud, and playing 4k video on 4k monitor would turn it into a vacuum cleaner.
The Air is completely silent at all times (it has no fan) and sits at 32°C while playing 1440p and maybe 40°C when playing 4k content.
It is of course possible, that this is all because the previous Macbooks were so bad (and due to hw decoding for common video formats) but I had similar "Jesus this is such a loud, overheating mess" experience with other laptops as well. But desktops have much better thermals already - so for you, the biggest difference would be the mobility I guess.