You're probably ideally placed to compare the TiVo-software (which powers the TiVo & V6 boxes) and the Horizon/360-platform - and I'm only saying that because a conversion from TiVo/V6 > 360 is a one-way choice that can't be reverted if you change your mind.
The V6 supports 4K/UHD exactly the same as 360 does - the hardware is identical, it's the software that differs.
As already advised though, to swap a TiVo for either a V6 or a 360 requires a physical box-swap in any case, it's just a choice of which software platform you want the box to run on. If you want to go the V6 route, you're best off asking for a box-swap as part of a package renegotiation - in other words, moving to a current bundle in exchange for the new hardware and an 18month contract. If you want the 360, then you can voluntarily request a swap from https://www.virginmedia.com/tv/virgin-tv-360
I'm a Very Insightful Person, I'm here to share knowledge, I don't work for Virgin Media. Learn more
Have I helped? Click Mark as Helpful Answer or use Kudos to say thanks