Bandwidth throttling at the source, or in a network device?

I got a little dilemma. We got this new device that needs to sync a sizable amount of data every day to a Azure Blob Storage. Apparently it will use some "Azure Blob Storage Sync Agent" to perform this action. This Sync Agent has a way of limiting the bandwidth directly in the source.

We could also tell the source to go through the proxy and limit the bandwidth there. We also have the option of sending it to the Firewall; but instead of limiting through the Sync Agent, we do it in the Firewall.

So we have three options of where we could limit the bandwidth usage.

I say we limit it at the source, i.e. through the Sync Agent, and create an ACL that lets the source bypass the proxy and go through the Firewall to its destination.

However we have some people pushing for the Proxy being the one throttling, and some pushing for the ASA having the throttling role.

What do you think?