Well here goes, I'll try and point out some of the main points.
Sky+ has one advantage over Tivo and that is that it can record two satellite channels simutaneously as they have basically shoe-horned two satellite receivers into one box. Satellite from a hardware point of view is an in-efficient medium because for ever channel that you want to view simultaneously, you need a duplicate piece of technology with the only exception of the metal dish. E.g. to view 2 x different channels, you need two satellite receivers, two LNB's (the plastic blob on the end of the dish) and two runs of cable from each LNB back to the receiver.
Tivo was created as a universal PVR, allowing you to connect any one medium to it rather than being dedicated to only one service like satellite. That means as your service provider might change over the years, you can still keep your PVR along with your recordings etc. Tivo supports Cable, Satellite, Freeview and the regular analog channels (1 to 5).
Whilst sky copied the Tivo concept with the Sky+ box, they did quite a poor job on certain aspects. The sky system still uses the rather cumbersome Sky Planner as the EPG (Electronic Program Guide). Not only that but by they have a cheek to charge for it as well unless the Sky Subscriber is on one of the top Sky Subscriptions! This is the same Sky Planner that users who have a non Sky+ box get for free! Tivo charges a subscription for its services because it provides a feature rich EPG with 14 days worth of guide data permenantly in the system rather than the 7 days with sky+. Tivo pays for this data which is supplied from a Media company called Tribune and they have to cover the Free call 0800 number which your Tivo uses to keep up-to-date so the overwhelming majority of Tivo users agree that the nominal subscription charge Tivo makes is not only justified but pretty good value for money too!
Because Tivo uses a proper database to hold the EPG data (and holds more information), this is what makes its other functions like Season Passes more powerful and reliable than the inferior Season Link used on Sky+. Other features on Tivo like Wishlists, Suggestions, Thumbs up&Down facilities etc are either not possible on Sky+ or would be wildly inferior using a basic system like sky planner as the database.
There is an incredible amount of extra functionality you can add to a Tivo by Networking the unit and adding 3rd party utilities. Additional functionality then to name but one means you can control your Tivo system from a PC anywhere in the world. Networking and adding functionality to a "closed system" like Sky is just not possible.
The Tivo Series 1 hardware (as used in the UK) is amazingly robust and reliable. Sure people have failures with the hard disk over time as these are prone to fail after a period of time due to it being a moving part. This is the same for any PVR though not just Tivo. In general, Satellite boxes can be very un-reliable. I used to repair satellite boxes and the cheap components used in the mass production of these units would often cause failures after a couple of years. For example a common fault was a Tuner Problem and the Capacitors in the Power Supplies drying out, this was spread across the manufacturers too, not just limited to one!
Moving on from reliability, (well slightly), the firmware based operating system that sky uses is not very tolerent to glitches. If users gets issues with corrupt recordings etc, the sky call center's common answer is to do a master reset. This unfortunately wipes all of the users data, recordings and all.
A few other sky+ down sides:
If you record a Pay Per View event, you can only keep this recording for a short period of time. A recorded program on Tivo stays viewable for as long as you want.
If you were benefiting from no charges for the Sky+ functionality by being on one of their top tier subscriptions, should you downgrade your sky subscription beyond a certain level you either have to start paying to continue to use the PVR or lose its functionality altogether, along with all the previous recorded material.
I have typed this off the cuff, so there's probably things I have forgotten to mention but its a start to answering your question
Regs
Dave.
Keeping the dream alive.