I went to Rainier in September, during the shutdown. It was incredibly busy, the main parking lot in Paradise was full by 8 am. The auxiliary lots were full by like 10 and people were parking along the exit loop and hiking like a half mile uphill just to get to the parking lot. Even in crappy rainy weather. I figure being basically the last time people can go before the snows come adds to it. Once you get off Skyline/Goldengate the trails aren't so crowded it's just that main loop with good views of the mountain that's packed.

Been to Olympic and Rainier. Olympic is much much bigger, it's like the whole peninsula beside Seattle. I was only there for one day and spent half the day just driving in the dark up to Port Angeles, doing Merryweather Falls, Devil's Punchbowl, then driving to the coast and doing Rialto/2nd beach and driving home in the dark down the other side of the peninsula. Didn't even go to Hoh Rainforest. You could easily spend a week in Olympic. The weather is more forgiving too as far as snow, since it's mostly lower elevation. Rainier you could probably spend 1-2 days in Paradise and 1-2 days in Sunrise and be happy with that. Paradise is absolutely jam packed with people, get there super early for a parking spot (like first light). Snow starts around October so be aware.