I cannot speak to price; I haven't comparison-shopped with this feature in mind. However, I have used various home gas ranges with either type of broiler. I'll go ahead and sum it up:
tl;dr: I greatly prefer an in-oven broiler.
First, positioning. Broiler drawers are typically located at the very bottom of the range, underneath the actual oven. This means that in order to place food in or take it out, you've got to bend all the way down to the floor. I hope the ergonomic challenge here is obvious, but I have safety concerns as well. If you have never tried to cook 10 pounds of flank steak in a broiler drawer, then learn from my experience: it's less than optimal. You will wind up bent over at the waist when pulling your finished steaks, end up tilting your pan and spilling meat juice on the way to the top of the range, and just barely manage to kick the drawer closed before your dog licks the exposed cooking tray. An in-oven broiler presents no additional challenges than you'd have with regular oven use.
Second: flexibility. Broiler drawers often seem to come equipped with an awkwardly-sized pan that's smaller than the oven itself. Sometimes this has brackets or rails to hold it in place in the center of the drawer. This is a stupid design that's difficult to clean, sometimes even difficult to remove, and limits your cooking space. The pan also rarely has any ability to move up or down, limiting your vertical space too. With an in-oven broiler, you can adjust the existing racks to get thick items underneath, and control how close your food gets to the heat source (and therefore how quickly it browns). I frequently kick on the broiler at the end of cooking with things like au gratin potatoes, to get a nice brown crust on top at the very end. I couldn't fit the pan I use into a broiler drawer, but with the in-oven version I don't even have to open the door. An in-oven broiler will also accommodate any size pan that will fit in your oven. Remember those flank steaks?
Regarding design, most gas ranges that I've seen with an in-oven broiler have two separate burners, a main version at the bottom that provides indirect heat to the oven box, and the broiler running along the top with a sort of heat shield to reflect its energy down into the oven. Drawers often seem designed to take advantage of only a single burner at the bottom of the oven, which provides both indirect heat to the oven box and direct heat to the drawer. This is mostly my assumption; I'm not an engineer.
This design could make drawers marginally cheaper (again, I haven't checked) but I think the advantages outweigh any price premium for the extra burner. I'll be so bold as to say that you will be very pleased with the difference if all you've ever used is a drawer.