The best pre-built argument is included warranty service for the whole machine but most manufacturers only offer 1 year included with an option to purchase extended plans. It's only really worth it if you don't have the skill or desire to troubleshoot problems as they arise. Most quality in-the-box parts offer 3+ year warranties so you get a longer warranty and the only downside is having to pull the part and do some service yourself (which, for many people, is the best way to learn).
Pre-built machines offer guaranteed compatibility between the parts that comprise them, where building a computer runs the risk of buying incompatible parts. This is easily prevented by researching what you're buying before you hit "Purchase" or slide your card. You wouldn't buy new tires for your car without making sure that they were the right size beforehand. Don't buy PC parts without making sure they all will work together.
If you aren't super confident in your troubleshooting skills I would say buy a pre-built, upgrade piece by piece as you learn more about how each part functions, and build your next rig yourself. If you have ever done hardware troubleshooting in the past or are confident in your abilities to solve potential issues (read: use Google) then building one yourself is the best option in order to get exactly what you need at the best price.