Take it to the sports car realm and ask yourself would you rather have a 350Z or a Challenger, since both cars are just the 4 door versions of each. The 350Z is more of the scalpel and the Challenger is the hammer.
I went through this exact debate 6 months ago, just with a bigger budget. 2013ish Chrysler 300/Dodge Charger w/Hemi vs. G37. My pros and cons...which I think would apply to yours too:
Dodge pros: Hemi, bigger car (more room for my kids and their stuff), runs on 87, quiet highway cruiser
Dodge cons: Heavy...and all the things that come with that...such as less nimble. Not sporty driving feel, thirsty
G37 pros: VQ is a stout engine, feels a bit nicer inside (you say it doesn't matter, but your mind may change), 95% of the driving "feel" of a BMW without the reliability issues, rock solid reliable, fabulous steering
G37 cons: A bit tighter inside, runs on 91+, thirsty
Personally, it was a tough call. I listed a pro for the G37 as feeling a bit nicer inside, as I was comparing it to a stripped down Charger...for me the 300C is really nice inside, so that was a pro for it. Yeah, the G gives up horsepower but it also weighs at least 500lbs less. So they're pretty comparable in acceleration. I was nearly 50/50 on which one I like better, and still kind of am. But what tilted the scales for me is that as much as I like the Hemi brothers, they can't dance like the G can. It just has that driving feel that makes you smile every time the road isn't a straight line. Truthfully, I wanted...and still want...a BMW 3 series, but just not ready to take the reliability gamble. The G37 is a great alternative.
In your price range, another concern I'd have is that a $3k cop car may be beat to E36 M3. You may have to search hard, but you can probably find an early G in your price range that's been well cared for.