The KVP-10 is the dual mono version (their model numbers are a little counter-intuitive). You can expect to pay a little more than twice the price of the KVP-20 for the KVP-10 with the phono stage.
When it comes to 'better', I can't say, thats too subjective. I like them both. Each one has their own character. If I were you, I'd go for the KVP-20, especially with your VMPS's. In modified form it's going to add some more texture to their presentation. On the other hand, if you are looking for extreme accuracy, the KVP-10 in its modified form may be more to your liking. Expect to pay extra though. Then when you add 6 Teflon V-Caps at about $70 each, it gets even more expensiive.
From what I can tell, the phono board isn't offered in the KVP-20, only in the 10. You can buy it separately. It comes in its own case. The phono stage is OK but for the money, the Graham Slee gear is better, IMO.