I do wonder if the new box design is to make it fit in with the designs of the Xbox One and PS4. I have a TiVo and a 2008-vintage fat PS3, and they both complement each other well with the curved design.
My parents switched to Virgin a few months and I had the impression that TiVo was good and fast, but when I briefly used it when visiting them I was amazed how slow it actually was! From watching a programme on Live TV to launching Netflix and watching something there was incredibly slow, taking something like a minute - they have a Chromecast too and it is almost embarrassing how much quicker it was on that than on the Virgin box.
To be fair I think it's always been a bit on the sluggish side, which disappointed me because the legacy Virgin/Telewest/NTL middleware was always quite cumbersome and slow, and this was supposed to be the fantastic upgrade we'd been waiting years for. Pretty much everything about the TiVo software is great, it's just a shame that the hardware lets it down. And in that time Sky have caught up and copied a lot of TiVo's unique features.
I don't use any of the streaming services like Netflix, apart from YouTube, but I don't think I would even attempt trying to load the YouTube app on it.
Can't take it for granted too much though. For now we have the great TiVo software with local recording to a hard drive. In the future we might have to use an inferior system that only lets you watch streaming content.