Fender is once again firing on all cylinders
If you're reading this, you've probably already read other online comments and reviews that talk about how, starting around 2008, Fender improved their designs and quality control and are once again churning out consistently high-quality instruments. I am here to tell you that it's absolutely true.
The new finishes they are using on the backs of the necks (as compared to the stiffer, more polyurethane-feeling finishes used in the 90's and before) play like a dream. It's as smooth as an unfinished neck. The bass I bought played fantastic right out of the box, with super low action and great intonation. I haven't even bothered to have it set-up yet.
All American Standards now come with Fender Custom Shop pick-ups, and the difference is noticeable. It still has that P-bass growl, but it has a warmer tone compared to the pre-custom shop pick-up models, almost like a cross between a p-bass and a jazz bass. The upgraded bridge rounds out a nice package. Also, I got lucky in that the bass I purchased, while new, was actually a 2013 model, so it came with an SKB TSA flight case as its standard, no-upgrade case. My understanding is that Fender's deal with SKB was terminated sometime in 2013, so not even all of the 2013 models have one, but I definitely recommend grabbing one if you can, since it's a nice free upgrade. That said, even the new cases that come with the post-2013 American Standard models are still a considerable upgrade over what you usually get with new instruments and are much better than those molded cases they used for years.
My only complaint is that the pick-ups still aren't quite as good, IMO, as the pick-ups in my '61 p-bass, but those are hand-wound pick-ups in a 53 year old piece of wood, so it's not really fair to expect a new bass to compete with that. And again, it's just a mellower sound, so it's not any worse, it's just different. I think I'm just addicted to that vintage sound. If you really want to replicate that tone, just get some Fender '62 Originals. I haven't heard them myself, but everything I've read indicates that a newer bass plus those will give you that tone, if that is what you're after.
Finally, I should mention that I didn't just play the bass I bought during my selection process. I also played a maple neck American Standard, a maple and a rosewood neck jazz bass, and one of the new American Standard Jaguar basses (all patiently brought out for me by the Sweetwater staff). So while your tone preferences may vary, everything I said about the quality of current Fender products goes across the board. Every single bass I played was consistently awesome, and I wouldn't have hesitated to buy any of them from a quality/playability standpoint.
Speaking of the Sweetwater staff, if you are in the market for new gear and have the opportunity to shop there (I don't live close, but I was in the area), I highly recommend it. Not only are the sales staff knowledgeable and professional, everything on the website is actually on-site, so while a larger chain store may only have one or two instruments of a given model in stock, at Sweetwater you'll be able to try pretty much any color/neck combination you want, and you'll be able to make your final selection from a much larger sampling of instruments.