I've always looked at it this way... (which makes me think of 'Young Frankenstein' with the "... walk this way" scene.)
1. You *need* a GFCI outlet on everything in your tank that can put electricity in the water, regardless of grounding probe or not. The GFCI protects *you*.
2. If you believe stray voltage is detrimental to the health of your tank's inhabitants, then a ground probe will take away that stray voltage. But if it is *not* plugged into a GFCI outlet, you will have no idea something is "leaking" voltage. When things "leak" voltage, it is just a matter of time before electrolysis causes it to leak nastier things that will for sure be detrimental to the health of your tank.
3. If you use a ground probe in a GFCI outlet, it may trip the GFCI outlet leaving you without power. Plan accordingly. It will trip at the worst opportunity.
4. If you don't use a ground probe, but use a GFCI outlet, if a device "leaks" voltage, you won't necessarily feel it or trip your GFCI if you just stick your hands in the water. You have to stick your hand in the water AND ground yourself. That's harder to do than it sounds. But if you do, your GFCI will trip if it's operating correctly. You'll get a buzz, but it won't be lights out for you.
To me, and I'm probably wrong somewhere there, those seem like the "for sure" things you can say. So it all gets down to whether or not you think stray voltage is a health problem for fish, and how you want to deal with when (not if) something shorts out in your tank. I've been lit up by a shorting powerhead in my tank. I had my hands in the tank for a while dealing with some algea when my arm touched a screw on my light fixture that ended up grounding me. My GFCI tripped. My arm was tingly. But the GFCI did what it was supposed to do.
One thing that is often overlooked in discussions about GFCIs... if you have some of your equipment on a UPS, you need to have a GFCI on the output of that UPS. Otherwise, if your regular GFCI trips as it's supposed to, the UPS will sense no power and turn on. If whatever tripped the GFCI is being powered by the UPS, then it's back live again and will start shocking again... until the UPS runs out of power or trips its internal breaker. Food for thought.