You should use the 10GB if you can. Never used these appliances before but I know most have an “assignment” of traffic types to each NIC like MGMT for 1GB and DATA for 10GB.
Check these links -
Exagrid | Veeam Backup & Replication Best Practice Guide
ExaGrid - User Guide for VMware vSphere
Hi @TK515 -
Your 1Gb NICs should be used for mgmt only, & your 10Gb NICs for data. Connect your 10 Gigs to your storage network. Also, depending on the storage protocol you're using (iSCSI?), you should change your MTU to 9000 (Jumbo Frames). And make sure EVERY device in the storage path is using Jumbo Frames (switches, Repo, Repo NICs).
Also, what Transport Mode are you using & how is it set up? Your Proxies should be configured for Automatic or DirectStorage for fastest method.