Benefits of Grill Pans
There's two (positive) reasons I'm aware of:


Aesthetics - those grill marks evoke fond memories for a lot of people, so the food looks better.  Studies have shown that when food looks better, people think it tastes better. This is why plating is so important in fine dinning. However - if grill marks don't evoke fond memories or you grew up with a griddled burger - then frankly these just don't matter.  
They rise the meat up out of the oil that its releasing.  This gives a burger, for example, more of a grilled texture and flavor as its not sitting in its own fat.  On a flat pan, the burger will release fat and then start to fry in the fat.  Its just a different taste.  No better or worse to me, just different.


There's (at least) three negatives that I'm aware of too:


There's less browning from a Maillard reaction because there's less surface area exposed to the direct blazing hot metal.  And frankly, the crust from the Maillard reaction tastes goooooood.
They are a serious PITA to clean.  If you've got one with fairly high, narrow ridges like the cast iron Lodge grill pan - if something gets stuck between the ridges it is really, really, REALLY hard to clean.
They smoke like crazy and you're indoors.  If I don't set off the smoke alarm with my grill pan, I know I'm probably not using it right.  Generally, you're trying to replicate the high heat of a real grill and you're often cooking something with enough fat to drip down and create wicked amounts of smoke.


For steak, I've really come to appreciate the taste of more crust from the Maillard reaction of a flat pan actually.  Not to mention then you can do great stuff like basting it in butter! 

Since getting better with my flat pans and griddles - I rarely use my grill pan.