Modern on-board NICs typically perform significantly better than add-on NICs going through PCI. However, for average single drive file transfers (around 30 MB/s), it doesn't matter much if at all. When you get into fast (newer, unfragmented, not full) drives and RAID arrays, you tend to notice the performance difference.
There are some on-board NICs which are bridged via the PCI bus, but this is an inferior design which is hopefully disappearing, esp. with the deployment of PCIe.
Using a PCI NIC and a PCI storage controller will of course compound the problem further.
There are other factors to consider -- esp. the CPU overhead of a particular NIC/chipset, but this can be mitigated with the very fast modern CPU's to some degree. Jumbo frames can also help with the PCI issue, but this is hard to set up.