Massive multiple-input multiple-output (MIMO) with uniform planar arrays (UPAs), which is often referred to as full-dimension (FD) MIMO, is being strongly considered for future wireless communication standards. FD-MIMO can control transmit and receive beams in both the horizontal and vertical domains and fully exploit the large number of antennas of massive MIMO. It is widely accepted that Kronecker-product codebooks using a discrete Fourier transform (DFT) structure are suitable to quantize the downlink channel at the user for FD-MIMO systems relying on frequency division duplexing (FDD). In this paper, we numerically study the characteristics of FD-MIMO channels using a three-dimensional (3D) channel model that captures realistic channel properties. Based on the study, we identify a limitation of conventional Kronecker-product codebooks and propose advanced channel quantization techniques that can further improve channel quantization quality.