I am not a fan of long recoil action semi autos, but the Franchi is a well time tested gun that works. I am not saying the action does not work, I am just saying I don't like the feel of them. Lots of people do, however. I escaped the infatuation with the old Browning Auto 5; I had one and much preferred a buddy's Franchi. The Franchi 48s are light guns and recoil will be more than many competitors similar gauge guns. I used to shoot a specially lightened 10 gauge BPS (as in machined) shooting the staunchest loads I could buy or build, and I still regularly shoot a 3" Magnum 12 gauge pump gun for waterfowl, so I am not a recoil wimp, but recoil does matter to a lot of people. It matters to me shooting targets. I believe that is why the 12 gauge version was dropped some years ago in favor of other designs. A 20 for most uses won't kick like a 12, and I don't care what the recoil tables with gun weight and load have to say about it. Total energy factors in there too. In my opinion it comes into play much more shooting targets than when wingshooting at game; my answer is adrenaline is at work on game.
It has been a few years since I shot any Franchi or even looked at a 20, and I do not know how well they handle light loads versus heavy, and I don't remember if you have to switch the recoil components around between settings for the different loads or not, but an owner should be able to tell you. They have not remained in production for coming up on 70 years virtually unchanged because they had a lot of problems. If you take decent care of it your grandkids will still be trying to wear it out.