I'm new to using a Weber gas grill as of this summer. Prior to that I assumed Webers were just overpriced compared to other options and that you were primarily paying for the name plate. At this point though I'm becoming a convert, at least for the older models (the jury is still out on the newest models from the past couple years as far as I can tell).
Regarding your question about "are they better", I think there's at least 2 aspects that people consider here. First is "do they cook better" and second is "are they built better".
As for cooking better, so far I think so, though it's not necessarily night and day (IMO). Prior to the 2002 Genesis that I'm using now, I was using a Vermont Castings VM400 (wife bought it before we got married so it wasn't my choice) and various cheap junk grills before that. I think the VM400 was a decent grill, and from what I can see it was probably comparable to a basic Weber when it was new. The 2002 Genesis that I'm using now does seem better, though. First, hot spots on the grill seem less obvious - meaning I think it heats more evenly which is nice. Second, the design of the flavorizer bars really does seem to mean less flare ups like the advertising claims. The flavorizer bar equivalents on the Vermont Castings were designed in a wave pattern, which meant grease and drippings could build up in the troughs. Thus, when flare ups happened, they tended to have enough fuel that the flare up would last for long enough to really make a sooty mess of your food. What I've noticed on the Weber design though is that even if I see a flare up from grease dripping, it lasts only a few seconds as the dripping is vaporized. The tent-style design of the flavorizer bars with steep sides means there isn't much build up there to keep a flare up going for very long. Most stuff that doesn't vaporize right away runs off the flavorizers and into the catch pan beneath, which is nicely designed to be easy to clean.
Another aspect to cooking better is a little more usage dependent and subjective, but the older Webers all used burners that ran from side to side (often referred to here as "east-west" burners). Basically every other grill I've ever seen (including newer Webers now) have burners that run front to back (or "north-south"). A lot of people here seem to prefer the east-west design, and it is especially preferred by people who use the rotisserie. I'm not one of those people (yet), so I think the east-west isn't as much of a benefit for me. I do think it helps provide more even heating as the gaps between burners is obviously smaller in an east-west design. However, it is a little harder to do indirect cooking as you basically are stuck with the back third of the grill for your indirect.
As for being built better, this is a definite yes (at least for the older models, pre-2005), and probably a big part of the reason why so many people love them. First, the design of the older models is such that there are really very few parts, and they can be disassembled easily. Some of the parts are essentially consumable (won't last on any grill), such as the flavorizers, burners, and some grates. Replacements for these consumable parts are readily available from many sources, making the grill easy to keep going. The non-consumable parts (firebox, lid, and frame) are built to last. The firebox is aluminum so it will never rust out (which is a big difference from a lot of cheaper grills). The frame can rust, but it is solidly built and can be cleaned up without much work and will stay mostly rust-free if you take care of it. The lid won't rust either unless the porcelain coating is chipped.
A big part of the maintainability of Webers from what I can tell is that they didn't change their designs much over the years, meaning replacement parts can be made that then fit a wide range of manufacturing years and models. That's an incentive for replacement parts suppliers because they can target a large market without having to have a different variation for each model year. This leads to parts being easy to find, both official Weber parts as well as aftermarket.
Anyway, that's my $.02 at this point. I was about to buy a brand new Weber this summer but realized I had an old one from a previous owner sitting on my deck already that I hadn't touched. I got inspired by the many great restoration threads here to tear that one apart and rebuild it, and I've been cooking on it ever since and have been very happy with it. It has an unassuming appearance (no stainless), but it's a classic look that I appreciate. I don't like stainless grills because to me they always look dirty (water spots, stains, etc.).
