And, you get basically the same amount of usable power either way, as 12 x 400 = 4800, and 48 x 100 also = 4800. The difference is that the 48V system may be a bit more efficient, with less loss to heat and certainly requiring smaller cables, which is a big plus (and cheaper).
I just looked on Amazon, and a 12v, 100ah LiFePO4 battery is about $350 (some a bit more $, some less, but that's a decent average for a quality battery). However, you need 4 of them to get the same usable power as from a single 48v, 100 ah battery, which costs about $1400. So, if you need 4800 watt hours of power, it's about the same price, EXCEPT you'll need larger cables for the 12v system, which costs more.
There are lots of people who think they save money with a 12 volt system, and that's sometimes true for very SMALL systems. But once your power needs start to increase, higher voltage is your friend, largely because it decreases the size of your cabling and will likely take up less space in the battery area. I built my system with 24V for these reasons. Looking back, I wish I had just started at 48V.