Outsourcing is always done for one thing and one thing only. To save money. What this means is that those who get outsourced are expected to do the same work or more work for less cost. It wont be apparent immediately, often you move over to your new organization with your salary and most of your benefits intact. What happens over time is salary increases and bonuses become smaller than they would have been had you not been outsourced. Also your new employer may not backfill workers who retire or quit. Other places they start to pinch would be training and travel budgets, maybe even redo your 401k contributions to give you less, etc. Over time they will reduce costs one way or another.
Hard to give advice on this since its a very personal decision. How confident are you that you can move to another job? Do you like your current job and coworkers? You need to factor these things in when deciding to move over or find a new employer. You may want to ask if you would be entitled to a severance package if you decline to move. If severance is a sizable chunk of money its another component to factor in.
Best of luck!