It's a mixed bag. Outsourcing is a great thing if you know what you are doing.
I managed a Fortune 50's key business unit outsourcing strategy for a few years. We were able to get some amazing rates and (more importantly) great commercial terms. There were a lot of benefits, too. Increased productivity with lower cost was one of them...but it's not as simple as just sending work to low cost geos. There is a lot of risk mitigation that goes into it and you need to have a plan.
First, low prices seem great but the bodyshop is going to take their usual margin. You think the sales teams are going to surrender their sweet, sweet commission? No way. This means that the workers doing your work are feeling the pain. You end up with expeirence builders who work cheap for six month and then go find a better job. Turnover is a real problem. If you just need warm bodies to crank code them maybe this is not much of a factor. If you expect people to stick around you will need to pay them a little more.
Second, your pool of cheap workers probably won't be the best quality. Expect rework and many, many hours on phone calls between 10:00pm - 2:00am if you are in the US. They will require detailed direction.
Third, the technical scope is maybe 20% of your problem. You need to really think about the business terms. How do you expect to manage warranty terms? IP indemnity? IP ownership of deliverables? Supplier's limitation of liability? Supplier's rights to terminate? Injunction mitigation/supply line protection (if you have customers that will depend on this work)? There is a whole supply chain/procurement component here that needs to be understood. A lawyer will tell you to take a hard line against risk. Practically, you need to determine where you can yield/concede "to get to yes."
If you choose to outsource, you need to spend A LOT OF ENERGY defining precisely what you need your people to do. They do not think and they won't problem solve...they're not paid to. They will take the shortest possible route to completing the deliverables in the scope as they are defined in writing. If you are envisioning something and assume that no competent coder would need basic, entry level directions to make your vision a reality, think again. "Certainly they will realize that they need to..." is never something you should be thinking. EVERY LAST DETAIL must be clearly defined.
As far as billing goes, do not agree to "actual effort", "true hours", "time and materials", or any other open ended billing structure. Your scope needs to be written well enough to get fixed cost, milestone payments, or time and materials with not-to-exceed pricing. Your supplier will bleed you dry if you just open your checkbook and agree to pay based on hours with no regard to deliverables.
If you go this route, consider hiring someone who knows what they are doing and take a lot of notes. You can manage this. It's not rocket surgery. Just skip the learning curve.