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Here's a list I recently thought up when comparing my TIVO Series 3 to my SA8300HD which I rented from Charter Cable for two agonizing years. The SA8300 is typical of these cable DVRs you speak highly of.
1) Season Passes. The 8300 HD of course lets you set recurring recordings, but you can't prioritize them like you can with TIVO. With TIVO, your higher preference recordings will get recorded in the case of conflicts.
2) Wishlists. TIVO will let you set Wishlists, like "Sitcoms" or "Scarlett Johansson", or "Atlanta Braves", and then you can peruse these as you like to see upcoming programs. You can even set Auto-Recording Wishlists, and your Wishlist items will record automatically. For example, I love poker, so I set up a Wishlist for "Poker", and TIVO will record any program it finds with poker somewhere in the description. Try THAT with the SA8300HD.
3) TIVO suggestions. TIVO will eventually catch on to the kind of stuff you like and start recording stuff for you. I love coming home and finding stuff TIVO has recorded for me. Sometimes I discover great shows this way. TIVO handles these shows intelligently (they never bump recordings you have setup, and get deleted if the drive gets full). Nothing even remotely like this on the 8300HD.
4) Recently Deleted Folder. This is entirely missing from the SA8300HD, if I recall. If you delete something and later wish you had not, you can retrieve your show. These shows get permantly deleted first, when the hard drive gets full.
5) 30 second skip. I love this button. Not officially supported, but works great. Not available on the SA8300HD.
6) Better video and audio quality.
7) It is a music and photo media server, meaning I can listen to my computer's MP3's and look at my photos using the TIVO. The 8300HD? Nope.
8) Podcasts. I can subscribe to any Podcast I choose using the TIVO and listen to them at my leisure. You guessed it - not available on the 8300HD.
9) TIVO remembers where I was when I stop watching a show. In fact, I can have multiple shows already started watching, and TIVO remembers where I left off with each of them. Like bookmarks, really. The 8300HD cannot do this.
10) Universal Swivel Search. This is very new, but I love it already. It lets you easily find shows similar to the one you are studying, and lets you link easily to other shows your favorite actors are in. I'm not doing this feature justice. You really have to see it in action. It's like having a direct link to an Imdb-type database.
11) The peanut remote is a thing of beauty. The keys are nicely backlit, with the words on the keys. There is a nice ribbing on the bottom so you easily tell which way is up in the dark. There is an aspect ration button. And most importantly, it is a learning remote, which means you can control your other devices. In fact, you can teach it some functions from the TIVO menu. Doing this alone I was able to control my TV's on/off, my stereo's volume, and the TIVO, of course.
12) Weather and traffic updates. No such thing on the SA8300HD.
13) TIVOcasts, which are video podcasts. Not a lot of content yet, but I love CNET and The Onion. They keep adding new TIVOcasts. MIA on the 8300HD.
14) Search by Title is MUCH better on the TIVO. IIRC, on the 8300HD you could only search by title on one specific day at a time. The TIVO will let you search your entire lineup for the next two weeks. Also, you can filter your search, or your guides, for that matter, by HD shows only.
15) Two weeks of guide data instead of one.
16) My 8300HD occassionally would not record something. When it did this, it would offer no explanation. TIVO has a handy recording history that explains why a certain show may not have recorded.
17) Show padding. TIVO will prompt you to pad live shows by minutes or even hours so you don't miss that last hour of the Academy Awards.
18) Intelligent conflict resolution. If, because of show overruns, a conflict occurs, TIVO will shave a few minutes off your lower priority show. Example (Dual Tuners assumed): Show A runs from 8:00-9:00. Shows B and C run from 9:00 to 10:00. If Show A ends up running until 9:02, most DVR's (including the TIVO of yore), will actually not record either show B or C in their entirety. The new TIVO will make a decision based on your shows' priorities, and will shave minutes off the lowest priority show. For example, if Show A is the lowest priority, it will cut off the last two minutes, and record B & C in their entirety. If Show B is the lowest priority, it will clip the first two minutes of it to catch all of Shows A and C. But you'll still get 58 minutes of Show B.
19) I can schedule recordings from the internet with TIVO. Can't with the SA8300.
20) I can download movies from Amazon Unbox if I choose. Not available with the 8300, although I did have on-demand capabilities with it.
Maybe I didn't convince you, but you'll find out yourself once you try some of these cable DVRs.
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