Gas grill compared to regular (high end) oven I've always been a charcoal guy, but as I'm thinking about buying a new grill I've looked at gas grills, with the convenience of cleaning, speed etc. 

But I still can't help to think a modern oven would be able to fulfill a lot of what a gas grill can do (oven broiler plus convection at maximum temperature).

There is no flame, and the heat is from below - but how much does matter?

Disregarding any non-food aspects (pollution, being outdoor, having a beer while grilling), how big are the differences?

Edit: Commenter moscafj below wanted some things clarified, he was spot on. 
My initial thought was to buy a charcoal grill, and for most other stuff use oven. I've had some thoughts about gas, but I always feel that it's just an "outdoor oven with an open flame".

Thus, I'm now comparing a standard outdoor gas grill to a new indoor domestic oven (with all the bells and whistles I can get).

The "drippings landing on hot bars" I've heard about, but that's basically the only thing.
While you are correct about the basics - both a grill and an oven can roast and sear, and it doesn't really matter if the heat comes from above or below.

However, there's some subtle details: 


An oven will have fine temperature control (via a thermostat).
With an outdoor grill you can impart smoke-flavors (either via
smoldering hardwood, or by burning drippings). While that's possible
with an oven, unless you have one SERIOUSLY good ventilation-system,
you shouldn't even try it. 
Grills also have the advantage of being outside - cookouts are much
less fun when you and your friends are standing in your kitchen,
staring at your oven.