There is very little chance that the new controller will recognise a RAID array setup by the old. Sometimes even switching between controllers from the same manufacturer or even the same range can cause the array to not be recognised.
This is one of the reasons I recommend against using the RAID support found on motherboards and cheap I/O cards (the other reason being that that are usually "fake RAID", combining the worst points of hardware and software RAID in one ugly package).
If you use Linux's software RAID then you can just transplant the drives to another machine and more often than not (much more often than not) it will work pretty much automatically. Sometimes a little manual intervention is needed (for instance: if the device node configured conflicts with an existing array in the new machine you need to manually reassemble the array, but this is done with a single
mdadm command). I'm guessing other OSs' software RAID solutions will transport between machines as easily, though Linux is the only one I know of for sure as I've performed the operation myself a number of times.
If you don't want to use software RAID then get a good controller card, then you can transplant the controller with the drives or get a new controller of the same type (this doesn't work with cheap RAID controllers because, as with wireless NICs, they sometimes silently switch controller chips between revisions so even though the box has the same part number they aren't necessarily compatible). Good hardware RAID's advantages over software RAID and "fake RAID" are better performance in some cases, complete OS independence, and (if you pay good money) safety features like battery backed cache/buffers.