In most rifles, the chamber is near completely closed until well after pressures have substantially subsided. I've experienced 9-10 casehead separations in my 223 rifle (OF'd internet brass, o boy!), and I didn't notice anything different until I pulled the trigger on the next shot and nothing happened, because the next round wouldn't chamber. Got to the point where I would automatically know what happened, clear the broken case head, rack in a round to extract the broken case, rack in a new round and keep going.
In most pistols, there's some unsupported area of the chamber where the brass can fail during peak pressure. In a plastic framed gun, this could blow the frame apart.
OTOH, the pressures can still be relatively high even when the action opens. As the case comes out, the pressures are lower, but more of the case becomes unsupported. This is how I suppose those 40 cases with guppie bellies that go more than halfway up the case are born. If the case blows out at this point, maybe nothing really bad happens.
Another thing that can happen with an overcharge is the case does not extract at all. The pressure is too high, so the case won't slide out of the chamber. The extractor slips off or tears through the rim, and then if pressures are still too high at that point, the case head can blow clear off like the cork out of a champagne bottle. So if you overcharge, you can have "catastrophic" brass failure even in a handgun with 100% casehead support.