Co-location can bring benefits but it carries risk as well. A few areas worth thinking about:
Flexibility - you can have any config you can build, no matter how odd or lopsided or unsaleable. Dedicated servers tend to be more mainstream, even when customised.
Hardware fixes - with rented dedicated servers you generally don't have to worry about the hardware other than being sure that the provider fixes things that break. With colo, you do. Who will carry the stocks of spares? Where will you get items from if they aren't in your stock. Do you need a third party to warrant and support the hardware?
Networks: often sold as 95% commits for colo, as opposed to the per-TB pricing common for dedicated servers. This can be an opportunity to save a lot of money as bandwidth use is generally pretty predictable across a providers user base, but you have to get it right.
Costings: if you are putting in, say, 10-20 servers, you should be able to save relatively significant amounts against dedicated servers if you do things right - but it needs capital and getting it wrong means a lot of wasted cash.
Commitment: buying kit means you are signing up for the long term - there's no cheap way out with £20k of server capex to pay for. There is also no-one else to blame for the vast majority of problems, if it's broke YOU need to fix it.
Risk - small scale colo (a couple of servers) can work but is much riskier as the cost impact of one of your servers dying from eg a bad motherboard is much higher than you might think - parts replacement, travel to datacentre or remote hands, long downtime etc. If you are unlucky (or have bought abused old kit) and get hit with bad hardware failures, it can wipe your annual profits out in a single stroke. Over a larger server base this will tend to even out, but a small/single server base makes for big peaks and troughs.
You'll notice I don't mention ownership anywhere as a good or bad point - I personally don't see it as anything other than an emotional or maybe a marketing issue. As long as you have use of the servers, does it matter if they sit on your balance sheet or someone else's?