The cap without the vent actually has a spring loaded valve inside it that should let the gas escape through the underside, so both those caps are vented. The one with the nozzle just carries the gas away from the expansion cap (via hose) so that it doesn't leave a pink puddle.
Anyhow, it sounds like you fitted a new one.
The expansion tank cap ought to release excess pressure, as long as it's not trapped inside the system. It's why you see head gasket failures resulting in a cloud of steam under the bonnet. That's the gas escaping out through the cap.
I can't open the links so I can't remind myself what your symptoms are... but a "burst radiator" is quite unusual compared to a burst hose etc. A radiatore is metal.. hose is rubber... the joint is fresh air held together with a clamp so if it's going to go, it has to go at a joint first, I'd have thought.
If the radiator is indeed "bursting" (photo?) then your problem is the radiator.
Is it mounted on the proper rubber lugs (bayonet sockets fit into a rubber "O" gasket which fits into holes in the support bracket. And is the top of the rad' mounted with rubber pads? If the rad' is flexing or getting jostled about, then that may be fatiguing it.
Do the rad's always go in the same place?
Is the system pressurised prior to failure? There is a bleed valve on the top left of the rad (as you look into the engine bay). When you have a COLD system... unscrew it slowly (so as it doesn't fall out.. since you won't be able to screw it back in when coolant is gushing out) until either coolant or gas comes out.
If you have gas coming out (it hisses) then bleed it until coolant comes out. Re-tighten the screw.. use the car for a few days and repeat. The gas should not return once purged. If it does, then you have a head gasket problem. I'm sceptical about HG... since you've had the kitchen sink and several engines worth of parts by the looks of it.
If only coolant comes out.. then the "burst" is not caused by gas pressure in the system. Similarly the water pump is unlikely to be able to pump coolant into the radiator if coolant is not able to escape (so it's not coolant pressure causing the burst). If you had a blocked rad' the car would also overheat eventually. Yours runs cool.
I'm guessing you have a new thermostat.. but a thermostat (good or bad) can't block the system and cause a pressure build up. It just diverts coolant through the rad or back into the block. One or the other...
Since you have no problems with the equally fragile heater matrix and hoses... I'm guessing your problem is mechanical stress on the rad. If the checks on the rad (bleed test for gas) only brings out coolant.. then take the bumper off so you can see the whole thing and re-fit the rad mounts from scratch.
If you look on ePer you will see diagrams of the entire setup. The rubbers are a few quids.. so it's worth re-building the assembly as Mr Romeo designed it. My hunch is that the rad' was replaced one time and put back incorrectly.. Also, if you have a/c have a look how that's mounted to the rad. You'll need to compare yours with some helpful person's on here.. it could be the a/c clag is stressing the rad' too, if it's not attached properly.