The current log viewer displays an unbounded amount of text in a single browser page. (This is certainly true if you ask to show the "full log". But even in the default mode, in which the head is truncated, a running build may then proceed to produce vastly more output. And if you actually need to see the top of the build, you need to switch to full mode anyway.)
Unfortunately many browsers do not perform well when confronted with many megabytes of text in a single page, and may even crash. Switching to the raw console does not necessarily improve performance, and you also lose hyperlinks and notes and so on.
It would be better to either display the log in a paginated mode, so that you would click arrows to move to a "previous" or "next" block; or logically display the whole log, but intercept scroll gestures to load a new section and discard the old one.
Unclear what the "page" size should be. You want it small enough to be effectively displayable on all common browsers; but large enough that there is not excessive network traffic and so that native scroll buffers are effective. Might need be tuned on a browser-by-browser basis, or made extensible by plugins.