The fundamental difference between Benelli M4 and Beretta 1301 is "short stroke vs long stroke" piston systems. After the shotgun is fired, the gas piston strikes the bolt carrier group back to start the cycling process. Benelli M4 uses a simpler short stroke design. There are fewer parts in the bolt carrier group. It means "less weight to move". Beretta 1301 is a long stroke design. If you take it apart, you can see that the bolt carrier group has many parts to move together. It means "more weight to move". Fewer and lighter moving parts usually translate to better accuracy. In addition, the more moving parts, the higher chance something could go wrong. It has an impact on the long-term reliability. Therefore, Benelli M4 is intrinsically a better design. Well, in theory at least. In practical usages, it probably doesn't matter to most users.
If you are worried about Benelli M4 not cycling lighter loads, you just need to change the buffer tube spring to a softer one (or cut off a small portion of the stock spring). Benelli intentionally uses a stronger spring in the buffer tube for long-term reliability on firing hot defense shells. In other word, it's not a defect in Benelli M4. It's a design tradeoff. If you fire A LOT of hot shells, you would need to replace the buffer spring more often on Beretta 1301 than on Benelli M4. If you uses a softer spring on Benelli M4, you'd also need to replace it more often than using the stronger stock spring. That's it.
For hot shells, you feel softer recoil on Benelli M4. For lighter loads, you feel less recoil on Beretta 1301. Depending on what loads you use, it has different impacts on the accuracy of your following shots.
In short, Benelli M4 is designed for combat. Beretta 1301 is designed for hunting and competition, and is being repositioned to "one shotgun for all purposes". Which is right to you? It's really up to you. For me, I don't hunt nor go for competitions. So, I have Benelli M4 as my primary shotgun and Mossberg 590A1 for apocalypse. But, I am also considering to get a Beretta 1301 Comp Pro and modify it into a tactical shotgun. That'd be a sweet shotgun!