In my experience, as a graphic designer, who has seen my type of work be outsourced (right in front of me) to some cheapo place overseas, I think it's best to just shut up and let the client do it.
Most of the time, they will get something back that is awful, and if they actually have an eye for quality, it'll make them better appreciate the work you do. You might even get some more work from them after they've satisfied their fantasies of cheap labor.
If they don't have an eye for quality, and they go with the garbage the outsource comes up with, then you probably didn't want them as a client in the first place.
This is a great policy. Sometimes a follow up at just the right time can really help too. Always be respectful, after all it's the client's choice, and be understanding that they are going to feel a bit embarrassed when the first results come back from the cheap place. Have a supporting story that lets them save face "I can see you're really a cost conscious guy, that usually correlates with a good sense of value too, while my stuff is a bit more expensive let me share with you what we do to make sure you will be satisfied ..."
The problem is that these clients have a particular budget. Perhaps they have $15,000 to spend. I tell them it's going to be $18,000. Someone else tells them they can do it for $7,000.
They go off and spend $7,000, then come to me because it wasn't done properly and say, "Unfortunately, it really didn't work out with these other guys - can you please, please help me out?" Now the problem is that they only have $8,000. Where before I might have been able to cut scope a bit to get down to $15,000; or perhaps they could have scrounged up another $3,000, they are now completely out of luck. And it sucks to see this happen to people.
On the other hand, sometimes people who charge less do a great job. As much as I'm not the cheapest person around, I'm also not nearly the most expensive, and I still do good work. To someone at the high-end, perhaps I'm one of those low-cost, risky alternatives, although I don't see it that way. The problem for the average client, though, is they generally lack the experience and understanding they need to properly evaluate all of their options.