So can you swap barrels on side by sides as long as ga Brand and model are same without having to gauge anything (like rifles you need to check headspace) as long as they close and lock up OK?

Most will require fitting. Snap-ons are rare with the older guns.
Bob Jurewicz

I can't speak for your home grown guns but since nearly all British guns were made pretty much individually (albeit cheaper guns sometimes in batches) you would be extrordinary lucky to be able to snap a set of barrels on to a different action.
Head space would be the least of your problems.
Even guns made as pairs aren't interchangeable.
Obvious, with modern machine made guns that are not hand fitted, the story may be very different.

I've done it to a skb barrels and fore end.

Very much a hit or miss thing with almost none that fit right without fitting them to the action. Sometimes even guns made very close to one another will just never work. I found a set of Sterlingworths barrels that were 40 apart by serial number and they would not work. Perhaps with a grinding wheel, JBWeld and a 40 ounce hammer they might. So try if you like but do not get your hopes too high.

Only way to find out is to try them . Some will go with a little work others wont . All depends on the gun and how they were made . I have done it with some guns but I have a pair of barrels for a Horsley side lock that I have offered on to a number of other Horsley actions with no success .

I have 3 modern (Browning) 20 ga sxs guns that none interchange.

From what I understand Valmet 412 O/Us have interchangable barrels. I have a Valmet 412 20ga. The barrels will fit very nicely on a friend's 412 12 ga. I didn't try his 12 ga barrels on my gun as he was the interested party.