From my experience (I own both) it depends on what you want out of the scope. The VX-3HD is simple, tough, and reliable — so good value / bang for the buck — sufficient for most hunting. But the VX-5 is hands down the better scope, and to answer the OP’s question, price: performance isn’t linear — once you’re past the VX-3‘s performance, you have to pay a lot more for small further improvements — so twice the price doesn’t equal twice the scope.
I would say there’s 3 main differences, and depending on individual needs, they’re not important to everyone:
(1) Low light
Side by side on a sunny day there’s not much difference at the same magnification, other than a wider FOV for the VX-5.
Once you start losing light or it becomes overcast, the VX-5 pulls ahead — in extreme low light the difference in clarity and resolution is almost startling.
(2) Mag range
Leupold series designation tells you the mag range — so a VX-3’s range is roughly three times the starting mag (3-9, 3.5-10, 4-12x, etc), a VX-5 is five times (3-15x) and the flagship VX-6 is six times (3-18x). The VX-3 is sufficient for most hunting, but some might want the versatility of a wider range — say for thick bush at low mag, then plains/ mountains/ targets.... using the same rifle and scope.
(3) side focus / illuminated reticle
A couple VX-3 models have side focus or an illuminated reticle, but no VX-3 model has both. To get both you need to move up to a VX-5 or VX-6. Some don’t care that they use their illuminated reticle infrequently, they still want to have it for the one time they might need it, say shooting into a dark background or shadows. Same with side focus — some don’t want the extra time and fuss to set it. Others want the ability to dial out as much parallax error as possible, especially at higher mags.
I also have a VX-6HD and it’s an outstanding scope, but there is less difference between it and the VX-5, compared to the difference between the VX-3 and VX-5. Again, law of diminishing returns.