When I first came to the outsourcing company I was perplexed and confused at the same time. The entire set of values I brought with me from a company that worked on domestic product was hardly applicable and required significant adjustment.
First thing that made me nervous was the absence of a defined development model. Each project was a small company per se with its own game rules. The set of rules depends on the qualities and experience of a leader (PM) and customer will. This is not arbitrary that I placed leader in the first place. PM is more influential figure in the project than it may seem to be. Few customers come to the outsourcing company having enough experience in software development, so they know how to organize the process. Most of clients are new to the domain and have vague idea about peculiarities and risks related to software development. A strong project leader can correct customer's vision of the problem to a decent extent.
Another difficulty was the dictate of the rules by customers. There were problems selling off testing services, especially in the difficult recession times. Testing is being seen as an additional cost. Testing does not create the direct value so it was perceived as a good candidate for cost cutting. Some customers even insisted that they will do testing on their own. I am not sure they realized what it would cost them. I am sure they would find a better use to their precious time. This looks even stranger if we think of a pitiful experience in testing they usually have.
The third problem is also related to the company being split into small reins with their own small kings. Introducing changes is a much more painful process. If it can be done only with enthusiasm in the "domestic" company, this is absolutely impossible in the outsourcing without a constant support from the top management. You simply find yourself bogged down in communication maze with all the parties interested, each of whom have their own vision of the problem, and each of whom used to adapt different kind of processes.
This is, in general, the core difference between testing and QAing in "domestic" and outsourcing companies. Having experience in both worlds I would suggest you to select the former if you want to learn building quality processes. I would suggest the later to those of you who value challenging environment, don't fear changes of rules during the game, and who is a good negotiator.