I have built 2 so far. It is always more costly to build yourself, because you are paying retail packaging for each component. If you have to buy a retail copy of the operating system, that's even worse.
Also, prebuilt computers are often sold at discount and may go on sale. It would take a long time if you wait for a sale on every component you need for your DIY pc.
You will also need to do some wiring between the motherboard and the PC case for the USB ports, power switch, reset button, hard drive light, etc. Since there is no standard connector for these, you usually have to connect them one pair at a time and sometimes you need to modify the connector to fit. The is the most dreaded part for me.
Also, if after you build one it doesn't work, you would have to debug the hardware. A small but possible risk. Both pcs I built worked the first time, so I can't share my experience.
You may find that some components interfere with others. E.g. the super cool CPU fan may butt against the RAM and not fit, so you have to return it and buy a smaller fan. There may be an airflow dead spot at one of the hotter running chip and you have to put in an extra fan.
The pros of building your own is, it can be cheaper by reusing components you already have. Many pc builders have lots of extra parts and they can tear down and older one for parts, so they may only need to buy a CPU and motherboard to build a new pc. In that case it could be slightly cheaper.
If you really want to build one, first decide on the CPU. You can tell which one gives the most bang for the bucks by observing which CPU is used most often by prebuilt pc. Or visit your favorite pc parts store and check user ratings for each components.
My suggest is, if you need the pc for real work, buy one. If you're not in a hurry and don't mind paying more, then you can consider building one.