Larry, here goes.
I'd say handling and agility are similar, though with hydraulic controls the Gazelle is perhaps a bit easier to fling around. Both are smooth in the cruise and vibs only go up when you try to go too fast. Neither will realistically cruise over 120Kt.
Both have stacks of power, but you'd have to look at manufacturers figures to see how much fuel you can carry with all seats full.
Regarding full seats, the Gaz has a decent sized cargo compartment even for 4 people's luggage, the H500 has none. Not even room for a toothbrush. Also rear pax have a pretty grim time in the Hughes. Its cramped, noisy and vis is poor. If you want to carry 4/5 people it has to be the Gaz, 3 in front in the Hughes is too cosy. The 'one cabin' layout of the Gaz is far better for pax, it also scores with easy access due low floor hight, getting into a H500 even on "low" skids is a three step climb, high skids makes it mountaineering. That said the Gaz is a lousy charter machine as the seating is still very military and the cabin nowhere near the comfort levels of even a JetRanger.
Gaz loses heavily on it's engine. The Astazou is a fine engine and far more robust than the Alison, but it time-exs at 2200hrs if memory serves and the cost of a recon one (if you can find one) is egual to the total value of the machine, so the economics just dont stack up. Parts may be a problem with the Gaz, few were made for civvy street and there may be certification/compatability problems on some items. DOC of the Gaz is said to be as high as a Twin Squirrel, H500 is pretty cheap to run (no hudraulics and good spares availability)
I always liked the ability of the Gaz to stop the rotor with the engine running, the disk is too low for rotors-running changes anyway. Fenestron is safer than a tail rotor and the ogre of fenestron stall is much overplayed as it is extremely rare even when provoked.
If I had enough money to buy a helicopter I would not have either, a Single Squirrel is leagues ahead in every respect. For practicality I think a B206 beats both too.
However if I had to chose I would prefer the Gaz, cos if I was that rich the cost of a new engine would not matter too much!
Does that answer the question?
Oh, and if you ever get one, can I come for a ride?