If you do choose the Keio, be sure to join their member's club in advance of booking. It gives some perqs and discounts and is free. The moving walkway to Shinjuku has quirky operating hours, sometimes both of them are going the same direction, often neither of them are running. But the Keio is right next to Tochomae station on the Oedo subway line.

The Hilton shuttle bus goes to a good location very close to the west exit and runs every 20 minutes throughout the day.

I've not stayed in either but would tend to regard them as roughly equivalent, upscale and definitely not luxury.