Most importantly, you can't have an LV spanning two different VGs.
Also, there's no tool to move a logical volume to a different volume group. You can do it indirectly by creating a LV on the target VG, deactivating the source LV, copying the raw content, and activating the target LV. And there's no tool to move a physical volume to a different volume group. You can do it indirectly by moving all LVs that use the PV to different PVs (with
pvmove), then removing the PV from the old VG and adding it to the new one.
These are reasons to have a single VG.
On the other hand, if you're ever planning to run your machine with only one batch of disks (perhaps because the 2TB drive has failed), this will be easier if the VG is still whole.
When you create a LV, you can choose which PVs it's on, but it's more cumbersome than letting it fall wherever it wants on the VG.
Given that the disk sets are intended to contain different types of files, I'd go for separate VGs.
You can make maintenance slightly easier if you ever need to shuffle VGs around by splitting each disk into several PVs. That way you have a chance of freeing one of the PVs in a VG to move it to a different VG. While you can shrink a PV (to allocate the freed space to a new PV in a different VG), it's somewhat cumbersome.