First of all cold start is going to be loud no matter what mode you are in. Try changing the modes while driving and you will hear the difference, maybe not so much at idle. I dont think there is any difference between sport and track for exhaust note but I could be wrong. According to the chart that is stickied on top of this sub forum, once you leave tour mode the valves stay open. Also, these cars being luxury cruisers have a lot of noise insulation, so the exhaust note is more noticeable outside the car than inside. Try punching it with the windows and sunroof open under an underpass and you will hear the blower whine and exhaust a ton louder than you think.
Me personally, I leave the exhaust mode on track in the settings so its always loud and then I let the steering and suspension go with whatever mode I set it. I usually drive in sport, as track holds the gears a little long for anything but super spirited driving and makes for a super low mpg and jerky experience long term. I do like the throttle blip downshift in track though. If I see someone I want to play around with, or I'm coming up on a tight turn or u turn where I'd like to hold a lower gear, I'll put it in track real quick. Also the launch control is only available in track mode.
EDIT - Also just noticed you have a blue V3... Sick color man!