You will see a though put increase in going point to point between two server, in removing a switch you will remove the store and forward latency which although isn’t high does affect though put more than you would think. You can use a non-switching hub or a cut through switch.
Fibre is overkill unless you servers are more than the maximum distance for cat 5e/6 which is 100meters or shorter depending on patching.
Also though put depend on your NIC , PCI,PCI-X or PCI express since that affects bandwidth as well.
A large boost is given by using Jumbo frames taking the frame size to 9k or can be larger up to 64k depending on the network card , not all NIC's support this feature with the usual frame being 1518 bytes with a MTU (payload) size of 1365 bytes, obviously the greater the MTU then better.
If you have multiple 1gig ports you can also look if they support Link aggregation or teaming where you can load balance over two or more network connections between servers
10Gig Ethernet is also total overkill since the cost is high and few devices actually can actually run anywhere near 10Gig, this is mostly used between switches or extremely high performance servers