Home Built is always cheaper, atleast if you look at what you get.
Lets say we compare a home built computer and a factory built HP computer with the same specs. Are there any differences between the two? Oh yes there are, examples:
* Lower quality/wattage PSU (sure HP put in decent ones, but any upgrade might not work because of lack of power headroom).
* Lower quality motherboard. One of my HP prebuilt computers was a micro-ATX motherboard sold for full retail price without ANY notification. Was missing alot of connectors, ports, expansion slots, etc.
* Often using slow memory. They sell computers by the amount of RAM, NOT the speed of it (the next point could have been affected by this also).
* Locked BIOS. Almost no settings to overclock/tweak the motherboard, RAM, CPU, etc.
* Low quality fans. Fans in factory built computers are often very noisy compared to silent fans, and in alot of cases there are not space for any extra case fans. Lowers component/computer longlivity.
* Tight cases. Often not more then space for 3-4 harddrives (if even that).
* CPU/GPU coolers. Often cheap stock coolers from Intel/GPU manufacturer that are often noisy.
* Low quality cooling paste. Often made of silicone and have a high thermal resistance.
There are some points I'd like to point out. Not ALL of them are true for factory built PCs, but many of them are. I might remember a few more if I really thought about it, these just came out in my head right now.
You could probally avoid all of them if you build a custom homemade pc for the same cost as a factory built PC. I understand that many people does not care about any of these, but I do.
If you search the web you can find MANY rigs out there with specifications on exactly what components you need to build it, for a very stable computer. It does not have to take more then a few hours to build a PC if you have someone that have done it atleast once before. If you are doing it for the first time yourself, it could probally take half a day. It is still worth it imho, and there are a lot of help to be found online.
Just my 2 long cents