Great analysis/explanation Blaugrana. BR was the first brand of clothes that I really identified with back in middle/high school, and they had some great stuff. I remember when the factory stores actually were outlets for unsold retail stock. Nowadays, BR has been overrun by folks looking for easy office-wear and smart-casual pieces, which is fine because that's what I use the brand for now as well. Some of the upper end items I still do really like, such as the textured suiting shirts and some simple outwear. I've got a hooded sweatshirt/jacket that I've been using for about 7 years now, and it still wears very well - can't find much else out there like it from any other brand. Like others, I'll stop by BR for some work-shirts on sale if I need to replace ones in my wardrobe, since they fit better into the office environment (a la Mad Men) than JCrew does. I also do like the Gavin chinos, though their fit has gotten a bit wider and material stiffer in recent years, not too happy about that. I do believe that the BR flagships in NYC and SF have a much better selection of goods that would indicate great quality and craftsmanship, but it's a shame they're not available in other locations. One thing I do like about BR these days is that they have been hosting promotional events at select retail shops to drum up excitement about the brand, such as Mad Men related things, Virgin Airways promos, or blogger spotlights - these are full of discounts, giveaways, and free food/booze.
JCrew stuff I'll basically only buy on discount unless there is something that I absolutely need at that moment in time. The materials used are generally higher quality than other options out there at the same price point, but I also have kind of lumped JCrew into the same wardrobe category (for me personally) as BR. There are some nicer items, but as pointed out, they are horrendously overpriced. The simpler basics are where JCrew shines, and select shirts are actually nice for the money if I use them as all-purpose casual or office. The shorts they have do fit well, so that's one area JCrew pips BR on. The one thing that I do NOT enjoy as much about JCrew (and this is sort of hypocritical) is that it is a bit more "exclusive" and "higher end". As such, people I know tend to over-love the brand and fawn about its products, even though it's all still the same crap made in Asia with all the same designs. The aesthetic is really nice and clean, but it's got the semi-hipster vibe going on that people want, where they want to feel like they're "in the know" even though everyone else is also "in the know". Brand dilution is certainly getting to JCrew in my opinion, so we'll see where it goes in the next couple of years.
TL;DR - I see BR as a solid office and basics outfitter, while JCrew is a yuppier basics and office outfitter with aspirations of being exclusive that charges a premium for urban-Americana-meets-wannabe-prep designs.