Each server decides based on it's own routing table which interface to use when connecting out. Unless you use some special features like bonding, you should get useful output by entering
sudo ip route show.
For example in my case the output looks like this:
root@mr-burns:~ ssh# ip route show
default via 10.60.0.1 dev em1
10.20.0.0/16 via 10.60.0.165 dev em2
10.60.0.0/16 dev em1 proto kernel scope link src 10.60.1.150
10.60.0.0/16 dev em2 proto kernel scope link src 10.60.1.151
127.0.0.0/8 dev lo scope link
I read this like following:
Let's say the destination is inside the network 10.20.0.0/16, it will use the interface em2 because of the second rule.
But if the destination is using the default gw because its not in any of the listed destination networks, it uses em1.