The older TiVo box has exactly the same OnDemand options as the V6. So all of VM's CatchUp & Boxset programmes from the same channels are all available if you follow Home > CatchUp, or Home > OnDemand.
The TiVo has its own inbuilt internet connection to make these services work, and your home broadband is irrelevant for this purpose.
Where the V6 differs, is having access to additional streaming apps. Much (but not all) of the programming on these apps is the same as what's available via VM's own platform.
The only thing to point out here, is that channels such as ITV & Channel4 especially, confuse matters here. To take ITV, they use the "ITV Hub" branding to mean several things.
If you watch ITV programmes on VM's CatchUp service, you often click on the "ITV Hub" logo and get "ITV Hub" branding onscreen. This does not mean you're watching on the "ITV Hub" streaming app, that's only available on the V6.
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