If you fly for a major carrier (Virgin for example) which operates both Airbus & Boeing, are the pilots type-rated in both Airbus & Boeing Aircraft or if you would have to choose what type of plane you would like to fly.
Most crews are only rated on (and familiar with) one type, so they’re not going to be switching between brands or even models without expensive retraining. There are some exceptionss where crews can be “cross rated” on both 757 and 767 or A330 and A340.
Hmmm…
My cousin flies for United and is cross-rated in the 737 and 757. Both are narrow bodies and have the same flight deck. I’m not a pilot, but flying a 757 and 767 (heavy) would seem much different in my mind.
But then again, I am just a cabin junkie 
–spud–
flying a 757 and 767 (heavy) would seem much different
The 757 and 767 were designed from the beginning to have a common type rating.
Ok, cool!
–spud–
If I’m not mistaken, pilots qualified to fly a 757 are automatically qualified for the 767 as well. I believe the flight decks are almost identical. That’s why the terrorists chose 757 and 767 routes on 9/11. The cabin layouts are completely different (single-aisle 757s & twin-aisle 767s), but the cockpits are the same.
As far as an Airbus pilot and a Boeing pilot changing over, that would be quite difficult, especially for the Boeing pilot, seeing as how Airbus planes newer than the A310 are all fly-by-wire, so the pilots use a joystick instead of the yolks found in Boeing cockpits. The Airbus pilots probably learned to fly on smaller a/c with yolks, so they wouldn’t have quite as much difficulty switching over, but it’s still a major change from what is familiar to them.
The Airbus pilots must have had egg all over their faces. My guess would be their flight training was on aircraft with yokes. (Sorry-couldn’t resist that one).
More so than the control unit (sidestick vs. yoke) are the differences in operation of the FMC. This would be a major block to having pilots current and scheduled to fly more than one type at a time.
Oops…I think I have egg on MY face… 
Thanks for the correction, dog!! By the way, I can usually hold my own when it comes to ATC/pilot lingo (spelling of “yoke” excluded), but what does “FMC” stand for? I’m thinking “Flight M--------- Control(s),” but I’m drawing a blank. 
Much appreciated!
FMC= Flight Management Computer
Pilots can either choose or the airline scedules pilots to fly an aircraft type.
Boeing and Airbus try to keep the cockpit layout the same in order to allow for pilots to opperate several version of the aircraft. Boeings 757 and 767 are common rated.The A330 and 340 are as well. With a little crosstraining it is also possible to include the A320 seriesinto the rating. However each type requires its own training and certification process.
Kind of like saying that; the difference between a Ford and Peugeot is the stereo system.
The FMS / FMGC is just one tiny fold in the whole book required to complete the transition, with the Airbus requiring much more data to be entered before take-off than that of most Boeings.
But there are major differences in systems, auto-flight, navigation systems and Airbuss have a much different approach to emergency/irregular procedures. Theres also the difference in learning the new flows and then theres the difference in performance and handling characteristics, the Bus has a better cockpit but twitchier controls and is not as fun to hand fly as a Boeing or MDD airplane and etc, etc.
Don’t know if it is still the case but Northwest used to have dual rated pilots qualified on both a domestic aircraft type and their international 747-400s. A pilot would fly rights seat on an A320 for example and would also be qulaified as an international relief pilot on the 747-400. My understnading was they could fly one type or the other in a given month but never both.