ZIPing files and directories can be very helpful. Make sure you compare the results when you do so.
FileZilla has the speed limiting capability, available under the Transfer menu.
However, there are issues with it. Most have to do with buffering.
FileZilla may indeed respect those settings but if the network itself has fluctuating speed you can easily find yourself in a situation where your speed-limited FileZilla has filled up a transfer buffer while the network or server interface is busy.
Then, when the network opens up more bandwidth there will be no speed limit to how fast the data actually moves through the subnet. This is crucial to understand. It will just blast data to unload the buffers as fast as it can.
In other words, you are doing everything you can to be a good neighbor, within your capabilities. Trust me, your network administrator respects that.
Sometimes, when this is commonly happening in-house, the Administrator's best approach is to make sure both systems are on a network switch with a nice high backbone capacity so it can handle the port-to-port transfers without affecting the rest of the network. That is nice and tidy.
However, if the transfers are going through the internet gateway or the same server interface that others are using, you may find that there is no simple way to avoid excessive contention by maxing an ISP's transfer cap or saturating the interface on the server.
Lately, the ISP I have been using simply enforces the cap all by itself. So you are not causing them any headache.
But the problem is your neighbors on the rest of your network that need to share that gateway or anybody using the production server on the same interface you are trying to use for large updates while it is on-line.
Usually, I suggest that scheduling is going to be the best solution. 4am transfers via sftp triggered by cron, for instance.
In all cases, make sure you work closely with your Administrator. Yes, they are busy, but the last thing they want is unexplained stoppages which trigger help calls. Trust me on this one. Short supervised tests and careful evaluation of the approach you follow will make for a happier experience.