I've worn both and I honestly prefer half chaps. They are softer and I can feel the horse more. They're cooler when it's hot because I can take the chaps off while I groom, etc. However, it's pain to put 4 things on my feet/legs instead of 2 (as with boots). I'm sometimes lazy and I just wear paddock boots & tall socks and no chaps, but most people don't like that feeling it seems.
Boots designed for riding do feel differently than fashion boots, like what you posted. You can find paddock boots for a similar price. If you don't want to spend a lot, Saxon makes a line of paddock boots that are cheap. If you really want to save, they make a fake leather version that both my kids have worn. They don't hold up like leather, but for my kids' growing feet, they wore out about the same time my kids needed the next size.