Well, mlabate, your post is a few weeks old, but I'll take a stab at answering it. Maybe some other folks will chime in too.
The advantage to the firebox is it supplies indirect head and smoke (if you're using smoke wood) to the main area of the grill. You don't run any risk of charring your meat, supposedly. I've found that, in practice, if I locate the meat too close to the opening to the firebox I can get some charring on the surface that's closest to that opening, especially if I lay the meat on the grill a bit early before the fire has settled down. A firebox usually will maintain a lower temperature to the main cooking area than having coals inside the main cooking area. If you're into the low-and-slow method of cooking, this can be important.
In my experience, using a firebox to barbecue low-and-slow requires a lot
of charcoal, but if I'm using hardwood only, it doesn't require as much. So if I'm barbecuing with charcoal and I don't feel like going through almost an entire large bag, I'll arrange a small-to-medium sized fire inside the main cooking area, but off to one side. I'll place the meat at the other end of the smoker/grill, well away from the fire. I'll then add soaked wood chips to the charcoal to give the meats a smoked flavore. And yes I do soak my chips. I've tried it both ways and if I don't soak them, they just catch fire and burn up without imparting any smoke to the meat.
So this second method above is one you can use with your grill for the low-and-slow indirect method, provided you have enough room in one of the chambers. If your grill has the capability to share heat between the chambers through an opening, you might try stacking up your fire right next to the opening and your meat in the other chamber. That might end up working the same as a firebox for you.
I've found that the smoky flavor depends on two things mostly: the type of wood being used and the length of time the wood is being used. It's often a matter of personal preference as to what wood gets used in some cases, and in others, it's a matter of what's handy. Me, it's usually what's handy. The first post in the sticky at the beginning of this forum area contains a link to a page that gives some good useful information on the various smoke woods. Here's another link to that webpage:
What Wood to Use
Since you don't like a heavy smoke flavor, you might want to try one of the lighter-flavored woods listed.
I don't know if a internal drip system is necessarily good or bad, but I don't think I'd go to the trouble. Some folks will place a pan of water under the meat for this. Others will even flavor the water with slices of oranges or other fruit. I used to use the pan of water under the meat, but honestly I didn't notice a difference between times when I used it and times when I didn't. Well, I did, honestly. The difference I noticed was I had more mess to clean up afterward when I used it.
So, I have a question for you: why two chambers? So you can do the low-and-slow thing on one side and hot-and-fast on the other at the same time?