Should I rent a trencher, or hire it out?
I have rented trenchers several times to dig long trenches. From the experience I can say several things that may help you bias your decision. 


Using a trencher is surely the way to go over hand digging. Hands down easy decision.
If you have to trench near a tree be prepared for a major pain in the tush. Small roots are no problem but if you encounter major roots it can be time consuming and can even get treacherous. On medium sized roots the machine can get bound up and if you are not paying close attention could even overturn the unit. So use caution.
If you have to trench down an embankment be prepared for some dangerous work as you approach the bottom of the embankment as the ground levels out again. The controls and holding bar of the trencher can come right down to the ground.
Depending on access to the to space up near the buildings you may find that some hand digging will be necessary. I found it useful to dig out a hole at each end that was several feet in diameter and extending right up to the foundation so that the trencher bar never had a need to come real close to the building. 
Good advice is to trench away from the building at each end and let the trenches meet out at come convenient crossing or merge point. 


On one occasion I elected to hire out the trench job to a contractor because I did not have the equipment to hoist a trencher over into the back yard where there was no direct access. In the end it was a good thing because after the contractor came to do the job, that they had quoted assuming use of their trencher, they ended up having to dig the almost 200' trench by hand because their unit was way too big to even work along the side of my house even if they could have hoisted it in there. 

So if you have a nice level terrain, no trees and good access on each end then renting may be a good idea. Do note that most rental yards will have the trencher on a trailer that you also rent. And if you do not have a suitable sized truck with a good hitch you will be required to rent one of their trucks to pull the trailer to your site. That will need to be figured into the cost comparison you make against contractor quotes that you get. 

As for deciding if it is cheaper to do it yourself ... that answer can only come from you getting several contractor quotes and then checking prices at the rental yard. If it is your first time ever using a trencher do figure on extra hours of usage time to deal with learning and encountering unexpected things ... especially with not having the site prepared ahead of time.