Sometimes I'll go back and listen to the radio call if something noteworthy happens.
For home games, I used to listen to the radio live - but now I have it running on my phone (so it is delayed 10 seconds or so) and will plug in my earphone if something happens that I want an explanation about... for example, if a play goes to review, I'll listen in to see what the announcers are seeing.
Honestly, I miss listening to the games live on radio. You pick up a lot about the game by listenting to the broadcast, plus get info about player injuries, etc. I don't do it anymore though because not it's just my and my youngest that go to the games. When his brother went with us, those two could chat and do brother things while I listened. Since the brother is on a mission now, I try to be more engaged with my son during the games.