Yes, there is a way. And its pretty simple, though it's hard to find it. 8)
For example, suppose your first account username is [email protected] and second is [email protected].
Open AWS Management Console as acc1. Get to the Amazon S3 bucket properties, and in the "Permissions" tab click "Add more permissions". Then add List and View Permissions for "Authenticated Users".
Next, in AWS IAM (it's accessible from among the console tabs) of acc2 create a user with full access to the S3 bucket (to be more secure, you can set up exact permissions, but I prefer to create a temporary user for the transfer and then delete it).
Then you can use s3cmd (using the credentials of the newly created user in acc2) to do something like:
s3cmd cp s3://acc1_bucket/folder/ s3://acc2_bucket/folder --recursive
All transfer will be done on Amazon's side.