Demeter, Shiira, Sunrise, Roccat, Stainless and Safari are all WebKit based browsers and will use the version of WebKit that is currently installed (normally the one that came with the currently installed version of Safari) for processing andy web content; that means that WebKit is responsiblye for nearly anything that is happening in the content part of those browser's windows; the "browser" is essentially a web browser user interface for WebKit. The browser shell can also change how much caching WebKit will be doing - this is what makes the biggest part of difference in speed. Some people determine the speed of the browser mainly by its launch time - Leopard WebKit will not perform as well as older versions of WebKit in that discipline.
That said you can "upgrade" any browser or application (like Apple Mail) that uses the currently installed version of WebKit with the upgraded WebKit frameworks that are provided by Leopard WebKit.
I test Leopard WebKit with Roccat, Stainless, Safari and Mail and those work well together.
The benefits of Leopard WebKit are currently a browser engine up to date with Safari 10 (lacking only some of the not so commonly needed features) and very importantly also upgrade HTTPS/TLS secured connections in order to fix all widely known security issues present in 10.5.8 .
In order to get an upgraded version of your WebKit based application just drag its icon and drop it on "Relink against Leopard WebKit" (comes with Leopard WebKit) and wait for the process to finish (that black and white wheel will disappear when relinking is finished).
Safari can be relinked as described above but it can also be used with upgraded WebKit by simply launching the "WebKit" application that comes with Leopard WebKit.
Relinking of Stainless will be possible with the next release of Leopard WebKit (available at
https://sourceforge.net/projects/leopard-webkit/files/602/Leopard/PowerPC/). Until then you can copy the "WebKit" application to your Applications folder and enable "Load frameworks from WebKit nightly build" on the "Advanced" tab in the Stainless preferences.
HTML5 video playback speed on youtube should also be quite good with Leopard WebKit - 720p playback works well on a 2.1 GHz iMac G5 as well as 480p on a 1.67 GHz PowerBook G4. Installing Perian might also make a difference - I always had it installed and don't know how playback performs without it.