Always like the 300zx. And comparing the two, it's more powerful (esp the TT version), and better looking. And it has 4 wheel steering. And its cooler.
It depends what you want to do with it. Also, what options do they each have...Turbo? stick? t-tops? They are both rear wheel drives. The 240 is an excellent platform for a drift car. Make sure it has the ser20de or ser20det ( t=turbo) motor. They produce the most power and respond awesome to bolt on upgrades. The 300 is crazy fast in a straight line and usually corners well. The V6 turbo/ twin turbo will have more power than you will ever outgrow.
If they are both automatics, I'd go with the 300 hands down.
You can research some archives on both vehicles at www.streettuner.com They can give you advice about bolt on's and hoursepower ideas as well.
Personally, I'd have to say the 300. The 240 was powered by a truck-spec 2.4 (high torque, low HP). I have not found a thrill quite like horsepower (owned a SVT Focus). Yes the 300 sucks at cornering (my SVT didn't, but it was 14.9 quarter mile), but you spool the twin turbos and WHOOOOSH, it takes off. However, if you are willing to spend the time and money to hybrid a 240, then better than a 300. Rear-wheel drive, light weight, and a better motor, can't lose (except 1/4 mile, depends on what you swap of course). When I had my SVT, I've raced some 300zx's, funny part is, my loss was only a car length or two at 60mph (when I shifted right). I wish there were some corners!
edit, I was going 60 mph, they may have been going 80+