Do you have access to the raw logs? When a visitor is human you will see the 301 immediately followed by a successful 200-- OR by another 301. Logs won't say what the request is being redirected to, but skip down to the next request from the same IP and you can see what they try next.
It's a little trickier with two domains because you're looking at two logs. But you can see patterns.
What you should see in the old site's logs is one 301 response per request, with no further activity on that site. In the new site's logs there should be an immediate 200 with no preceding 301.