Having run both, we went with the renting option (I still have dedicated servers here if you want some
The reason we went back to renting dedicated machines was time, staff and infrastucture. While it was cheaper to own the machine and pay for the bandwidth used etc, with the rate the hardware is changing it actually cost us money as we were then left with obsolete machines on our hands within a year or two. Cost played a factor as we had to have 24x7 datacenter coverage, an office at (or near) the datacenter etc etc etc.
Simple math here:
Server: $2,000 * 40 machines = $80,000
Rack: $700/month x 12 months = $8400
PDU Remote Reboot units - 2 @ $1,000 each = $2,000
Bandwidth: 20Mbps Connection @ $800/month = $9,600
Costs about $100k for the first year (that's IF you can keep your 95th percentile bandwidth at 20Mbps and lower), and that doesn't include control panel software, server licences etc etc.
Compare this to 40 rented dedicated servers at say $150/month with bandwidth included - $6,000/month or $72k per year.
Where the advantage of OWNED equipment comes in is that on the 2nd year, you don't have that $80,000 expense on server hardware, and now your cost is only $20k/year in datacenter fees.
Granted, I'm looking at it with a number of machines and not just one machine, but you can extrapolate the numbers.