There is a strong parallel between them - the solution to Z340 depended on the observation (independently by two people) that there was an unusually high number of repeated bigrams at width 19. For K4, there's an unusually high number of repeated bigrams at width 21 and that pattern is much stronger than with Z340.

The problem is nobody has guessed the method for K4 (and the message is much shorter at 97 characters). With Z340 there was the important context of Z408 and the underlying method of homophonic substitution. With K4 if people get into it enough, they usually try the polyalphabetic substitution of K1 or K2, or combine that with transposition ideas, influenced by K3, try that for while, and give up. Nobody will know the method for sure until it's been solved.

Another parallel: Z340 "rates at about a 7 or 8 out of 10 in difficulty to decipher" according to Oranchak. When Ed Scheidt, the designer of the Kryptos codes, was asked the same question about K4 he said "I would think like a nine, it's way up there".