Books and media = Amazon. Free shipping over $25 dollars, reviews and great product information.
Someone else's junk, car or real estate = Ebay. That piece of treasure thats someone else's junk is on ebay. Or if you have the time to hawk a "no reserve" auction to take a chance that the item fits the description go to ebay.
Never had a reason to use Amazon. Used to get extra gun barrels, mags and whatnot from Ebay, til they banned it all. Now I use gunsamerica.com or gunbroker.com, even though it's nowhere near as good for odds n ends as Ebay once was.
Equipment? Depends on what. There are a number of things I can buy locally from small business owners with which I either have a rapport or genuine liking. Sadly, there are also a number of small businesses I don't care for, and then I try to support the wellbeing of online folks with whom I'm friendly.
In general, though; Nothing I really think I need from either place. I'll buy my toys and other doodads from wherever (locally, online, that hobo that hangs out under the bridge), but nothing important.
Both and sometimes neither. Depends on what Im looking for. I can find a used book on Amazon for 70% off the new book price. I got a Jeep torch lighter off Ebay the other day for $5.34 w/free shipping. Retails for $30.00.
Ebay can be tricky especially with some sellers inflating the shipping costs to make more money.
I picked Ebay, but in the last year I haven't used either one. I am sick of the BS that both companies provide. For me, I will pay a little more local, or find a web retailer that is actually respectable. Sorry little sellers and dropshippers, but time is up and fast bucks are over (read: stolen money). At least from me.