Originally Posted by thatgreekdude
Bigger stacks can call considerably wider, basically because they can do so without risking there tournament life. It's a good thing for you as you have a good opportunity to double up against them.
Exactly this. The thing to consider too is peoples' play with different stacks will usually differ. Some people are able to adjust their play accordingly and play well no matter what stack size they have. However, most people don't play optimally all the time and as a result, can be exploited. The tendency is to, as thatgreekdude said, open up their range and play hands with an approach that may be exploitable.
The key is to, as others have said, pick your spots carefully. If you have some history on their play, that works in your favor too. Sometimes you have to push back against them to keep them honest.
The bottom line is, play the game you play that is most comfortable for you. Sometimes you'll be able to double-up, and sometimes it won't work out. At the end of the day, if you feel that you did everything you could have done and not felt like you could have done something differently, then you'll be fine. If you also brainstorm with others on key hands (either hands you doubled up on or hands you busted out on), you may find a different perspective helpful for your game when you are faced with the same/similar situation in the future.