I own a VK3i (office system) and a VK30 (main system). It's worth mentioning that the two preamps are not priced the same, so to some degreee it'll depend on your budget.
The two preamps are quite different; the 3i has four 6DJ8/6922 tubes while the 30 has six, although both preamps have remote controls the 3i is limited to volume only while the 30 also switches inputs, and of course they look quite different. When you pop the hood it's clear there are more (and better) parts used in the 30 than the 3i.
In terms of sound the two do have a "family" resemblance that is BAT's signature sound. Smooth, very slightly rolled off, non-fatiguing presentation and great imaging. Both preamps benefit from tube-rolling and are quite sensitive to interconnect (power cords don't seem to make a lot of difference). I find the 30 has better control of the bottom end and has a wider/deeper soundstage than the 3i; the differences are quite obvious but both units are terrific products in their own right. If you have the budget, buy the 30 but you won't be disappointed in the 3i if you choose to go that route. Click on my System for a feel for the associated equipment I'm using. Best, Jeff