NOTE: The TRANSFORM effect currently has the option for bilinear and bicubic. It would be good to add nearest neighbor here, but that should not be the ONLY place where it is available. The Transform effect still has severe issues with buggyness, instability, and choppy movement. Again, it is important that the MOTION effect has the option for Nearest Neighbor.
Currently, Premiere uses the Lanczos method for intrinsic scale and rotation. Lanczos is an exceptionally high-quality interpolation method which generally yields better results than bicubic, bilinear or nearest neighbor. From reading the forum post, it seems that up-scaling is the real issue here. I suggest looking at the Detail-Preserving Upscale effect in After Effects. It does a really good job and gives you some parameters to tweak to fit your specific content.