The following conflicting info has me wondering who is the most reliable source for updates.

I have an HP computer with an Intel wireless card.. Last week the HP support assistant reported a driver update was available for my wireless card. Having recently checked for updates, I did so again. The update driver function said my driver was up to date.

I called HP support and their explanation was that the Intel driver was a basic driver and the HP driver was superior. I installed the HP driver and all works well, though I did not notice any change in performance. Today, Windows update tells me I need to update the driver for the wireless card.

Any thoughts on which driver is the right (or best) one to use?

Use whatever works best for you.
There really is very little to be gained to updating drivers as soon as they are released.

Personally I never use the Windows Update site for drivers of any kind. The few times I did back in the 90's when I first started with PC's were a disaster. If you see updates from MS for graphics cards, sound cards, networking or anything for that matter, just ignore them. Using the PC manufacturers website is always the best for hardware that came with the system, since they tweak their systems in many instances that can make original drivers buggy. Unless the PC manufacturer (HP) sends you to the hardware manufacturers site (Intel, nVidia, etc.) use their stuff. Also, video drivers for a motherboards chipset are not the same as video drivers for a card. Often HP will send you to the card manufacturer for the latest drivers, and if you put a newer card in your PC definitely go to the cards site.