When would it be advisable to consider moving to Intel Server NICs instead of using the on-
Well, first: Normally what you call latency in SQL is irrelevant , this is not a gaming system or a financial market distribution, and the SQL side latency will be larger than the network one.
Second, that totally depends on the crappiness of your hardware. Seriously.
I have some motherboards here - both small server stuff (Micro ATX C32 Mobo) as well as gaming (Asus ROG I7) that both have high end on board NIC chips from... Intel ;) Some cheaper ones use broadcom etc - there you may have driver problems. But the Asus Rampage IV Gene, for example (which I use) is sold with "GameFirst with Intel Ethernet - The speed you need to pwn". ;) Beat that with a SUXOR server NIC - no PWNing ;) Joke aside, that is a decent network chip. Device manager identiies it as a 82577LM.
What areas could possibly benefit? (i.e.,throughput,latency?)
Latency. POSSIBLY - but it wont be something you realize on SQL Server, and it will be a theoretical gain. Throughput - well, given how fast a processor is these days, and how low the 1gbit throughput is, no. You can max it out on a tablet anyway.
Next step is a 10G intel card, around 300 USD for a dual port.