I'm going to disagree slightly with your term 'shootout'. When I think of the word, I usually think of it in the context of a one-on-one battle. It may not be a simple one shot affair but it's still basically face-to-face. You're describing a gun battle, which isn't the same thing at all. In that sense, I like the one in Rio Bravo and also Silverado, which does end up as well with a nice showdown between Kevin Kline and Brian Dennehy.
To stretch the definition even farther, I'd like to mention the final confrontation in Kurosawa's Sanjuro, which is a western in all but name. No guns but, man, is it fast! Don't blink or you'll miss it. It's over in less than a second and involves our hero (Toshiro Mifune, of course!) drawing his sword left-handed for a reverse right to left push-cut. Brilliant! Check it out.