Performance is not the deciding factor.
First I should say, asking a SOAP-vs-REST question is a little cockeyed, because SOAP is a XML envelope format, and REST is an architecture. So I will make a little assumption and suppose that you are really considering SOAP-vs-POX or SOAP-vs-JSON or SOAP-vs-some other data formatting approach.
The deciding factor should be this:
Do you now need, or will you need in the future, the SOAP envelope?
The SOAP Envelope allows things like framework-provided encryption, digsig, routing, and authorization checks, among other things. You can of course, do those things with REST (or more accurately, with plain-old-XML, or JSON, etc) but you have to do more work yourself, to make that happen.
If Performance - whatever you construe it to mean - really is your #1 criterion, then you should probably abandon SOAP and POX and move to protobufs or something else optimized for performance. These can be faster to serialize and faster to transmit.
If you think this answer is "too philosophical" and you really want hard figures, well, then I suppose you'll need to conduct some tests. The actual perf will vary greatly on the toolkits you choose, the shape of the messages, and the extra data services (like encryption and so on) that you use. But in the end, perf won't be, or shouldn't be, decisive either way.
If your SOAP toolkit is 20% easier to use. debug, and maintain as your POX toolkit, then you should use SOAP, regardless of the performance. People (coders, architects, testers) are much more expensive than CPUs and networks these days. You can always buy another 2 cpus, or a bigger network, if necessary, and if your design is correct. But you can't buy 20% less time developing, at any cost, if your framework is hard to use, or if it drives away your people. Unless you are running a geo-scale network, you will do better to optimize for the people, instead of for the network.