Portable air tank or 12V air compressor?

I just did my first autocross in our new 335is Coupe (won 2nd Place in TS!).

When I used to autocross my S2000 I had a portable air tank that I took with me. It's well past the expiration date on the tank and the tire chuck doesn't work anymore so I decided to buy a new air tank. But after some research a 12V air compressor would probably be smaller and more versatile. I'd like to know what other drivers use that autocross or track their car.

What makes more sense, a portable air tank or a decent 12V air compressor? If a 12V air compressor, which one?

Also any recommendations for tire pressure for autocross for an E92 with staggered 18" high summer performance Michelin Pilot Sport PS2 ZP, 225/40 ZR 18 88W front and 255/35 ZR 18 90W rear tires? Tire pressure on the door jamb is 33/41.

I started off using an air tank. It seemed more "professional" and allowed quicker filling/adjustment (as long as I had good pressure). I also was concerned about running down my battery.
After that tank developed a slow leak and caused me some problems, I've gone to a 12v compressor. A decent quality compressor will be smaller, lighter, and will work plenty fast enough.