I wouldn't say you're going to save oodles of money. That was true 5-10 years ago, but nowadays there are budget desktops available from so many reputable places that you can really get great deals online, especially if you don't already own a non-OEM windows license (and aren't using a free operating system).
What you really gain, other than some technical experience, is the ability to customize exactly what goes into computer. What motherboard you want, what (and how many) video cards you want. How many pci-e slots you need, what cooling options you want, how many hard drives and in what raid configuration (if necessary), how many ram slots the mobo has and what the max capacity is, etc.
Building a computers great. I've done it in the past and will continue to do it in the future. And it has its benefits, but in just straight savings you're probably not going to get all that much, unless you build a top of the line rig. But if you just essentially build a budget PC, you can probably get a comparable budget pc elsewhere.