Not really. The way crypto works in DVB-CSA is a little tricky to explain but here goes:
a) The crypto in the STB (Irdeto, Nagravision, Videoguard etc) listens for entitlement control messages in the incoming transport stream. The content of these ECMs is unique & proprietary for each crypto scheme.
b) The proprietary crypto scheme cracks open the payload and extracts a descramble key. The descramble key is just a random 64 bit number.
c) The descramble key is plugged into the CSA algorithm to decrypt the video / audio content. The key is only good for a second or so and then another one is sent.
Steps b & c) are common to every DVB-CSA implementation and a) is unique. A cable company can transition from one form of crypto or run a couple side by side, sending ECMs for both kinds of boxes at the same time. A cracker might be able to compromise a) in one scheme but it would not necessarily help them crack the others unless the schemes were related in some way.
Theoretically two ECMs for different boxes do contain the same descramble key so if you know the key from one ECM it might help you crack the other, but I expect that every scheme ensures to salt (put random stuff in and around the key) to stop this. More modern STBs also do 2-way crypto (i.e. they need a cable modem) so it's not enough to just read what's on the wire.
I don't think it will be long before someone starts selling brute force devices that simply try every possible combination of descramble key until they find the right one. Then it won't matter what crypto is in the box because DVB-CSA will be completely broken. If that happens the shit will hit the fan since you'll be able to plug a CAM of any kind into bog standard satellite / cable receiver and watch ANYTHING.
I expect at that point that Sky et al will have to replace their older boxes. I imagine their more recent boxes may be capable of DVB-CSA2 & 3. I don't know much about either but I expect the keylength and crypto algorithm is a lot stronger to resist brute force attacks.