Twitter client Twitterific can be a little sluggish, it doesn't make as much use of the iPhone's location-awareness as Twinkle, and the free version features (acceptable and unobtrusive) ads, but it gets our vote because it's so very polished.
It looks beautiful, there's lots of attention to detail, and the inline help system is superb. We love the inline browser, so tapping on URLs doesn't bounce you out to Safari, and you can get info on your Twitter friends. There's no background notification obviously, but that'll be killer when it's rolled out. An ad-free version costs £5.99.