It seems to me that the drow will have to be very strong, or perhaps have a way to cripple one of the ships, because smart PCs will temporarily join forces with the other adventuring party to defeat their common foe. But it all depends on how you want it to play out.
Do the drow attack the PCs, slowing them down and giving the other group the advantage?
Do the drow attack the other group, effectively getting rid of 2 enemies at once?
Do the drow attack both simultaneously?
I'm not sure what the capabilities of the airships are, but I might structure events like so:
1. PCs are flying, spot their rivals ahead of them. A short "chase" skill challenge allows the PCs to close the gap. PCs are probably making plans on how to take out the rival group as the ships close.
2. Drow surprise attack! The drow ram their ship into the PCs' if the PCs lost the skill challenge. Otherwise the rivals get rammed, or the target is random.
2a. The PCs' ship is locked with the drow's. They have to fight off their attackers (maybe convincing the rivals to help out), and then pilot the drow ship to the party.
2b. The rivals are fighting off the drow. The PCs might help them out, or might zip on ahead, laughing at their good fortune.
3. The party. It's hard to say how to handle this without knowing what the PCs are equipped for. Can they find the key without being detected?
3a. If they fought off the drow, the rivals are here and have a head start on locating the key. The PCs might be able to use this to their advantage, letting the rivals do all the work and swooping in at the last moment to nab the key.
3b. If not, the drow or the rivals show up at an inopportune moment, revealing the PCs to the giants.
Either way, it sounds like a good opportunity for a stealth and/or social skill challenge.
4. Having located the key and maybe dealt with the other groups, the PCs have to figure out how to extract it and themselves from the situation. Bonus points for leaving the other team stranded.