There is a nifty tool https://github.com/larrabee/s3sync which can transfer files very quickly with S3, but it reads all files into memory. If you're transferring lots of large files this process will quickly get killed by the kernel due to OOM.
The next best thing I have found is to tweak the AWS CLI to use aws s3 sync
as fast as possible.
# ~/.aws/config
[default]