Rainier climbers, making an ascent during the popular June to August window, are usually perfectly well served with a light plastic boot such as a Koflach Degre ($255), or a moderately heavy leather boot such as the La Sportiva Makalu ($245). Anything heavier than that is simply overkill, and apt to be very uncomfortable on the lower portions of the climb where you are apt to be hiking on bare, rocky trail.
In contrast, a climb on McKinley REQUIRES a heavy, expedition-weight boot, along with full overboots. The minimum is probably something such as the Scarpa Inverno ($290), combined with an overboot such as Outdoor Research’s Brooks Ranger ($125). The Inverno also has an optional alveolite liner ($200), which might be recommended for an early season climb on that big, cold mountain. Otherwise, boots such as the Koflach Arctis Expe ($355) work fine as well.
And an Inverno would not be terribly out of place on Rainier. It’s the closest thing to a plastic boot that handles a pretty wide range of conditions. Better to have too much boot on Rainier than not enough on McKinley, I suppose. Still, I think even the Inverno is overkill for Rainier, save for the technical routes or maybe climbs on the cold side of Rainier, such as Liberty Ridge. But if you want to get just one boot for both mountains, this would work.