Halo was an absolutely huge driving force in getting consoles on the map for first person shooters. The genre probably would have taken a lot longer to mature on consoles without it. It consistently led the charge for FPS games up until Halo 3. After that, Call of Duty took over with Battlefield on its heels. Though it wasn't just about the genre. Had it not been for Halo, Xbox might not have lasted beyond one generation. Xbox has been very influential and there is no telling where the industry would be today without it.
That being said, Grand Theft Auto III really set the stage for a juggernaut of a franchise that has set the bar for open world games and being proof of how much money a company can make off of sheer quality. Open world games are increasing in quantity, size, and scope. They're everywhere now. Rockstar knew back then that they would be the future of the industry and they really haven't stopped making them since.
Unlike Halo whose influence, commercial success, and critical reception has diminished and few FPS titles today take inspiration from its original framework, Grand Theft Auto hasn't budged. Its commercial success has only increased. Its influence in open world games is felt constantly with entire franchises like Saints Row and more recently Watch Dogs trying to directly emulate it. It is consistently scored among the greatest games of all time with each entry. Grand Theft Auto III was truly the beginning of that.