Ridden up the west side 4 times, down the west side 3 times and down the east side once.
J is right about the headwinds. It was no easy pedal to St. Mary once I got down on the flatter portions heading east. Descending west you will have to hit the brakes a lot, if only for the traffic in front of. Good thing is that you can take the lane and the steeper parts.
Whichever way you go, do start early. If you are the around the solstice, you can pretty much start out around 5:45 a.m. without the need for a headlight to see, even on the west side. If you go west, you cannot go beyond Sprague Creek Campground between 11 a.m. and 4 p.m. Sprague Creek is much smaller than Apgar, which is a zoo. Nice hiker/biker spots on the infield. Bear boxes and tent pads. When I was there in 2017 there were also some camp chairs and an axe to split wood, which the host offered to me for free along with some cookies his wife had just baked. The lodge is within walking distance, but don't expect to find much in the way of groceries at the camp store. It's mostly junk food and trinkets for tourists. The food at the lodge was actually quite good in 2017. Had a nice salad, mussels and steelhead filet. Line up before the place opens for dinner so you can get a window seat.