Hi John,
I recently upgraded my BJ8 radiator and looked at what was available at the time, including aluminum vs copper, recore vs new, and eventually decided on recoring but with slight modifications to improve cooling. Note that the original radiators were flat fin type cores, not louvered and from what I have seen of one or two originals they were four row, staggered tube units (others please help, as I'm not sure exactly what were the original cores, as these were shown to me by the fellow at the radiator shop who had experience with the british radiators and was confident they were the original cores, but they could have been late model cores too, upgraded from original cores). Also, I'm an engineer, Mechanical, so I may get a little technical, so I apologize if I get too involved.
I don't have experience with the Moss radiator, but it seems to be consistent with what you would expect with a 'modern' recore from a heat transfer perspective. It has a serpentine fin core, tubes spaced at 1/2 inch intervals from pictures that are available, and I called Moss for more details like number of rows, size of tubes, number of tubes, etc. but no one could help me with the details.
Aluminum pros:
1) Light weight, so its easier to install or remove but saving gas or added acceleration is pretty minor
2) Heat transfer? No, but from what I've gathered, since copper cores have a solder interface between the tubes and the fins which impedes heat flow, the performance of copper vs. aluminum is about equal with the edge to the copper core.
3) Stiffer, the aluminum core is much stiffer than the copper, but I'm not sure this is a benefit since the frame of the healey is so flexible, the radiator should be somewhat compliant so it isn't trying to keep the front of the car aligned all by itself. I believe the steel original radiator side pieces are designed with flexibility in mind so minor twisting or pulling doesn't fatigue the copper bits.
Aluminum cons:
1) Repairability, it is much more difficult to repair an aluminum core since removal of the tanks is cost prohibitive.
2) Maintenance, if you wish to have it rodded out to remove blockage or fouling, again, removing the tanks is difficult.
3) Vehicle value loss, retaining the originality of the vehicle is important for resale value, and IMHO the original core with the Coventry Radiator works badge on it is very classy.
Recore vs New - generally if your tanks are in good condition, recoreing is much cheaper, but beware of which core you choose when you have it redone. There are many options available which most will leave to the radiator technician who is doing the work. In general, if you select the four row, staggered tube, flat louvered fin core it will look almost identical to the original core but with the louvering, will provide a significant upgrade to the original. It should be 2 1/4 inch deep, which is the maximum the side panels will allow without modification. This core is available in the US, and if your shop cannot provide it, find another shop. I, on my first try, left it to the tech, and wound up with a 3 row, serpentine fin louvered core which was insufficient to cool the car. I wasn't paying attention, and was busy at work so went with what he recommended. I wound up redoing it with a 5 row, flat fin, louvered unit by modifying the side panels to accept the deeper, 2 7/8, core. It looks almost as a stock, original core, and the bottom tank didn't need modifying, and I'm quite happy with its performance. It will still be marginal, however, on a very hot day if stuck in traffic but I'm continuing to study that issue and hope to identify the base reasons when things are warmer here in Oregon.
Anyways, good luck with your selection. Whether you choose Aluminum, upgraded recore, or new, the cooling performance should be adequate if your car is in good condition and you have sufficient air flow through the radiator.