To add to the previous replies, just do some homework on what TV360 involves, and choose whether to convert or not, with an informed mind. Migrating to TV360 is a one-way process.
TiVo-firmware drives the legacy-TiVo and newer-V6 boxes, and is very recording-centric with a good streaming option added on.
Horizon-firmware drives the TV360 and is fundamentally different to TiVo. It's very online-centric with a recording option retrofitted.
There are many difference between the two approaches, and opinions vary wildly with pros & cons both ways. Please do some research, and whatever you choose - do so on an educated basis, not driven by some fancy glossy.
Your contract bundle should not be affected in any case - all you're choosing here, is which software platform your TV box runs on. It's analogous to deciding whether to use Apple or Android for your mobile phone.