Having run Brand You of hosted dedicated servers in various countries, and not using both options of in house and colocation my response may be a biased but for really good reasons!
Biggest advantage is almost no capital costs. You pay for recurring costs as part of a package plan. You only have to supply your system and any extra things you wish to send. They take care of one time chargeable installations and they have a package rate which covers electricity, security and multiple layers of bandwidth. Also its easy to exit the plan or upgrade or downgrade the plans. Also if you find a new provider with better rates or deals, transferring is much easier.
If you had done all of this in house , the easiness to move out would be very difficult and expensive as the capital costs are huge and then you also pay for operating expenses. Eventually if your business model is small and time bound, a data center in house does not make too much sense.
In my opinion just rent out a dedicated server from a provider – comes out to be cheaper unless you are looking for multiple servers in which case colocation might be better. I personally advise not looking at a colocation since within 3–4 years your hard drive will start generating errors and you will have parts that need replacement. Colocation typically won’t cover those costs.
Hope that helps! Happy hosting!