Try the Genelex gold lion KT77. I tried a bunch of EL34's and 6ca7's in my VTL ST-85 and the KT-77 was way better. Never tried the KT-66
It will be different, but as for "better" that is hard to say. The change will depend on the EL-34 you choose and what you think of the sound. In very broad terms the sound should tighten up and emphasize the sound in the midrange and higher frequencies. The sound may become more detailed.
NOS EL-34s are really quite rare these days and very expensive. Which tube were you going to use?
The Genelex Gold Lion KT77 recommendation is a very good one if you want to explore the EL34 type without the uncertainty and expense of the more sought after NOS tubes.
If you do want to try NOS EL34s a good bet is the East German made RFT. They were branded and sold by lots of companies including Siemens and Telefunken. The supply of them seems to be greater than the exotics and the price lower. As with any vintage tube you'll want to get them from a reputable dealer who can test and match them. Actually, that goes for the KT77s, as well, even though they're current production.
Whether you'd prefer EL34s to your KT66s, though, is a question no one here will be able to answer for you.