Is there a difference in reliably and performance with onboard Gigabit Ethernet LAN made by Realtek, Marvell, Intel?  Is one better than the other?

For what purpose?
If this is for a home computer, then no.

Really depends on the chip, as there are many different chips made from each company
but as long as they have (or there are) bugless drivers for their chips, I'm content
as for current onboard ethernet, they should all be the same unless you are utilizing your computer with some super fast connection or are using it as a dedicated server - then I wouldn't use onboard
if I did have to choose one, my preference would be Intel as I had great experience with their NICs
 
I always think separate NICs are better (as in performance) than their onboard counterparts (I could be wrong though)
my old mobo doesn't have onboard lan and I would disable it if it did

 
Onboard is the same as the card its self - they use the same pci/pcie bus etc.
 
Intel has the advantage of equal or better throughput aswell as lower cpu usage

Well...it really comes down to this: a LAN chipset is only as good as the interface that it is connected to. A PCI NIC will have roughly the same performance as a onboard chipset connected through the PCI bus, and a PCIe NIC will have roughly the same performance as a onboard chipset connected through the PCIe bus, but a PCIe of either will KILL a PCI of either, even if the bus is only of x1 width.
 
Now, moving on to your question of brands...I've never seen an Intel onboard chipset, so I really can't address that, but, both Marvell and Realtek make good stuff, so you're fine with either. Just remember, PCIe > PCI.