Depends how much data you have, how important it is and how sensitive it is, those would be the three things that would affect what sort of service you use.
The "use your own server" is good on the keep your sensitive data safe model if you take adequate precautions, but you are going to need some redundancy in RAID and some sort of tape backup procedures at the other end to make sure your data is protected.
If you data isn't that sensitive/important etc you can get away with it.
Using a 3rd party, if they are decent, gives you peace of mind in terms of redundat data, backups and security of your data, balanced against giving your senstive data to the 3rd party to look after, however most of the big guys in the sector are used to handling all sorts of sensitive info and often encrypt it anyway.