In fact, there is very little difference in build quality between the major motherboard manufacturers, they all use the same German and Swedish machines to populate pretty much identical PCBs with pretty much identical SMDs and other devices.
When looking for an AM3+ board, an important thing is to check CPU support for the board. Some AM3+ CPUs, in particular the FX8300 series, are power hogs, and if the manufacturer says that the chip that you want to use is supported, that means at stock speed, not overclocked, so calculate a margin. If a manufacturer certifies the board for an FX8370, you can run an overclocked 8350, but I wouldn't trust it to run an FX9370 overclocked. If a manufacturer certifies a board for an FX9590, it will run everything you throw at it, because the margin will be calculated by the manufacturer, as it was an AMD requirement to certify boards for FX9590 only if that meant the board was stable above 5 GHz.
If it's for an FX6350 or below, it doesn't matter all that much, and you can get a cheap board, these chips, even overclocked, do not draw that much current at all, they draw less current than a Phenom II. The FX8300 (which is an OEM-only CPU) draws as much as a Phenom II X4 965 and similar overclocked, and can run without overclock on a cheaper board, but all other FX8/9 series, require a more expensive board with a good power assembly. The more expensive boards are all the same in terms of power assembly, Asus has the marketing, but not much different specs, in fact, the SMD MOS-FETs that Asus uses, produce a bit more heat than for instance those used by MSI and Gigabyte, and are basically the same as those used by AsRock. Gigabyte and MSI use MOS-FETs with a slightly lower specific resistance, making them heat up less and provide more constant power conditioning. Fact is that the difference between all of those boards is really minimal, the variances between individual boards of the same type from the same manufacturer are probably bigger than the variances in average performance between similar boards from the different major manufacturers.
AMD chipset boards are generally quite good. The reason is that in 2009, when Intel paid a couple of billion dollars to AMD to avoid a court procedure, they settled with the agreement that Intel could produce systems for third parties, but AMD couldn't. The result is that Intel makes its own motherboards and doesn't regulate a lot when it comes to third party motherboards based on chipsets, because they set the standard by making their own boards, and Intel boards are available all over the planet, in much more countries than Asus/Gigabyte/MSI/AsRock/EVGA boards, so they're not too worried. AMD can't produce their own boards except for engineering purposes, so they regulate what manufacturers of AMD chipset boards can and can not do. This means that manufacturers are producing fewer AMD boards, because all boards pretty much have to be full featured, and AMD doesn't allow manufacturers to produce boards that block chipset features, so the differentiation is made by the selection of the chipset rather than by the quality of other parts on the board. AMD also regulates the power assembly specifications and the certification for CPUs. So basically, if you get the AMD chipset board that fits the CPU requirements, with the chipset that has the features that you want from your board, just pick the board you can get the best deal on. On caveat though, Asus has notorious bad support, they try every trick in the book and then some to escape warranty liability, and they don't follow up too well on BIOS updates. In fact, Asus has made a deal with Microsoft in 2009 (aka the "Runs better on Windows EeePC deal") that prohibits them from delivering an official BIOS that enables hardware virtualization (which is undoubtedly the most important feature of any modern PC). On AMD boards, they have to implement it because AMD requires it, so they have tried just about everything to block hardware virtualization, from swapping "enabled" and "disabled" in the BIOS, so that users would set it to "enabled" but it would be disabled, and when it was set to "disabled" it was in fact enabled, to loading the BIOS with bad tables, so that hardware virtualization wouldn't work, and when AMD and users forced them to correct that, they wouldn't release the version of the BIOS that had working hardware virtualization as an official BIOS release, but would make it available as a "beta" version. There always seem to be some kind of annoying issues with Asus BIOS's. If you don't want to deal with that, don't buy an Asus board.