Hello.
If I understand you correctly, you have one ethernet card for Admin and backup, and another ethernet card for Applications (Data VMs). then you should also have vlan to separate the admin and backup traffic.
The speed of the ethernet card should match the speed on the external switch port.
Another point to check would be the firmware and driver that the ethernet card has and if these levels are the ones recommended by VMware and/or the card manufacturer.
Although it is basic, if possible the Backup server should be connected to the same external switch where the ESXi host and the vCenter server are connected.
Have you increased the GB of the backup that is performed?
In the external ethernet switch where the ethernet card is connected where the backup and administration traffic goes, can this port be monitored to see if it is saturated during the backup? What values are displayed?