Regardless they both cost money to run. Looks like the cheapest NAT gateway[1] is currently $0.045/hr which is about $32.76 per month. Then you also get charged $0.045 per gigabyte transferred as a "data processing charge" in addition to standard AWS data transfer charges.
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I work for AWS.
Just as an FYI you don't have to use a NAT instance there are also NAT gateways which I find easier to manage: http://docs.aws.amazon.com/AmazonVPC/latest/UserGuide/vpc-na...
Regardless they both cost money to run. Looks like the cheapest NAT gateway[1] is currently $0.045/hr which is about $32.76 per month. Then you also get charged $0.045 per gigabyte transferred as a "data processing charge" in addition to standard AWS data transfer charges.
[1]: https://aws.amazon.com/vpc/pricing/