Difference between NCBI's /genomes and /1000genomes
The simplest difference is the scale and range. The aim of 1000 genome project was to provide comprehensive library of human genetic variation. DNA of individuals coming from different ethnic groups, geographic locations were sequenced and the results of the study were published here. 

Genomes from NCBI come from different organisms and the number of sequenced individuals differ between species (including human). This database is constantly growing. Detailed description can be found here.