I have been involved with both of these differant types of system. I'll admit I was only ever on the recieving end of CHORES whilst I was a Crewing Officer. ( Sorry remembering is bringing me out in a cold sweat!)
However it did make life a lot easier for keeping track of high hours.
We were given every day the running 7 day totals in decending order with highest at the top. Simple? Yes, but effective. You can identify those crews with high hours and ensure their following 7 days at least have a chance of staying legal. I believe we can all exscuse, within reason, a 7 day bust to the 'authority', but I can't think of any possible reason for someone exceeding a 14 day limit.
To this end CHORES was good at helping you to constantly monitor and amend your duty hours. As far as other advantages to the system I couldn't comment as I never got that involved.
Paper systems and spreadsheets are generally I feel more time consuming, and would not be able as flexible. However this doesn't mean that they would be any less effective for you. As mentioned by nearly everyone it depends on how many crews you need to keep track of, and your available resources to do it. At the end of the day as long as you can satisfy the authority that you can keep control of your FTL's they will be happy with whatever system you use.
[This message has been edited by You splitter (edited 16 May 2000).]