The most immediate benefit I see to working for different divisions of a same corp is that you get access to higher quality/level agents, either sooner or closer to your current base of operations, or again that you get more chance to refuse missions.
Let me explain: I'm Gallente and need to build up my standings towards a Caldari corp. I operate in a pocket of a Gallente region where this corp has at least 4 stations within 2 jumps of each other at max, counting 6 lvl2 agents spanning 3 divisions. As soon as my standing allows, I switch to the "next highest quality" agent in the area. On the other hand, I refuse to deteriorate my faction standings towards the Federation. So, when current agent asks me to go blow some fed navy ships, I politely refuse and wind back to the previous agent. This way I don't have to stop asking missions for 4h (..).
That's just one reason to refuse missions, there are certainly others ;-)
It's off topic, but I'd like to complete DarinaS answer: you get a storyline mission after running any 16 missions for a corp, from any mix of divisions or agents that you like, provided those 16 missions are given by same level agents.
Another more-than-good reason to work for different divisions occurs when you start working with R&D agents, as they significantly differ from the other divisions' agents. Again, it may be off topic, so I wont linger here. Check the EVElopedia on that matter if interested.
Regarding your "it always seems my advisory agents are the highest quality" remark, it may be due to the fact that some npc corp only assumes a part of its objectives in some area.