Nikon 55-200 VR or Nikon AF-S Nikkor 85mm f1.8G?

Which one is better in terms of good performance both portrait and landscape photography?

Neither is much use for landscapes, and the 85mm may be a little long for portraits.

The 55-250 offers some flexibility in portrait work, but you'd need a bit of space to get the best out of it.

For landscapes neither. You want a wide-angle 10mm, 12mm for landscapes.

For portraits you'll be better off with the Nikon AF-S 50mm f/1.8 prime lens or, if your budget allows, the AF-S 50mm f/1.4 prime.

Another benefit of either of the 50mm primes is the fast aperture which is useful in low-light situations.