How much does actual branding weigh in these days when it comes to buying a bicycle of an established brand (i.e from a bicycle store)? Or is it all about the components and the brand is just a label?
Major brands make a wide range of bikes, some of which are great, others not so much. To further complicate things, some brands license their name to bso's on top of their normal decent quality sales (e.g. Schwinn). So, you can't really rank them on quality in a meaningful sense; just compare a subset of models across manufacturers.
That being said, what are you getting when you buy brand X? Well, it's similar to buying a car. A brand is associated to some extent with prestige, quality and value. Also, how much support you can expect if things are going south (e.g. if there is a frame defect, will the warranty honor it). Giant probably would; Random chinese shop on Alibaba probably won't exist by the time you complain. You are putting a good amount of trust in a bicycle to actually be safe and able to do what its supposed to; that trust is easier to put in when the bicycle is from a quality manufacturer.
At a given price point, different brands will have different components and frame+fork designs. Some of the price is due to marketing/brand name (e.g. if you had an Audi and VW badge on two identical cars, the Audi one would sell for a bit more) and the cut the shop needs to take to stay in business. Other parts of the price are engineering and components.
Note that if you spend more on one part, it means you're going to have to cut somewhere else. Thus, you need to compare bikes (after riding them, hopefully) in order to see whats a good value and fit for you.
Also, note that spending more or going for a less well known brand is not necessarily good or bad. For example, REI used to sell some pretty decent touring bikes under their less well known Novara house brand for considerably cheaper than the usual Trek 520 / Surly Long Haul Trucker / similar.
In addition to what @Batman says, a bit part of quality (to me anyway) is quality of service. At the brand level, this will depend largely on the countries distributor and how well they support the local bike shops.
Ask you LBS which brand they feel offers better support, which dealer would they rather work with to sort out a warranty claim. Which dealer holds parts vs has to order them in from offshore. Ask "If I broke a frame in a crash, which brand would I rather have?", "If the frame cracked, which brand is most likely to honor the warranty quickly and painlessly?".