The big benefits...
You have a view of the band. You can see 'holes' to QSY or key up in because you see who is around and the width in use. Makes it very easy to find your locals on 75m or 160m too because you can see at a glance the very strong signals.
The filtering is just insane. The orange window is the center frequency I'm listening to. You can click and drag the low or high side of the passband out to 10kHz total width. If you get interference, you can 'see' it and just drag the filter edge where it stops and it's a brick wall filter. If someone is 2.5 khz away, you can just eliminate them.
Not in my version yet, but will be soon, many of the SDR options have a dual-receive function so you can listen to two at once.
Recording...not in my setup yet, but some have it all integrated. Not only just recording the conversation you are tuned to, but the actual raw spectrum width you are monitoring. So when you play it back, you can tune through the playback.
It ain't cheap though...hardware based wide band SDR receivers like mine run from $600'sh for the SDR-IQ to over a grand. The Softrock is the cheapest alternative if people are kit builders...a fully set up Softrock is <$100 for RX/TX kit last I looked. A single band receiver is only $20 or so.