I dislike the comparison to IE6 because it's easily shot down with
    the many ways in which the situation is different.

Inseparable from an OS version and falling behind the state of the art.

What else is there?

Being pretty disingenuous to compare IE6 with WebKit in terms of implemented features. Many websites had to be specifically coded for IE as it wouldn't render correctly many basic parts of HTML/CSS. WebKit is deficient mainly in the newer, less popular features.

Also Microsoft would unilaterally add proprietary features and tie their software to it e.g. Outlook/Sharepoint which then encouraged corporations to do the same as well. Apple actively participates in standards organisations eg. one for Web Components:

http://www.w3.org/2015/04/24-webapps-minutes.html

Legitimate questions:

    Many websites had to be specifically coded for IE as it wouldn't render correctly many basic parts of HTML/CSS.

Was IE6 demonstrably less compliant than other contemporary browsers? I recall - similarly - sites that were "Best viewed in Netscape Navigator at foo x bar resolution."

    Also Microsoft would unilaterally add proprietary features

IIRC, IE6 added XmlHttpRequest, which - though there were other workarounds to accomplish the same thing - enabled AJAX.

Do not other browsers even today add their own features (e.g. browser-prefixed CSS properties) prior to standardization?

    ...and tie their software to it e.g. Outlook/Sharepoint

Okay, that's definitely bad.

Falling behind was never IEs worst 'feature'. Standards compliance, security and speed were much bigger issues.

    Standards compliance, security and speed were much bigger issues.

In these respects, how did it compare to other contemporary browsers?

When it was released? It was the best (ok IE5 on Mac may disagree). Seven years later (when IE7 finally appeared) it was worst.

Initially well, but soon very poorly, because IE6 remained a contemporary browser for an unusually long time.

Distilled down to the core, the fundamental problem with IE6 was the five year chasm where development was completely stalled. When the version was finally bumped in 2006, so much time had elapsed that the solution was unsatisfying for everyone: changes so major that compatibility was problematic, but still insufficient to bring it up to speed with its competitors.

Safari may not be implementing bleeding-edge features at the same rate, but at least the engine is being continually developed and improved.

  > But Safari absolutely is falling behind other browsers in
  > API support and could well end up holding the web back

I am afraid that hastily releasing half-baked APIs and moving on to the new shiny things will do web more harm in the long run. IMHO web is suffering a huge identity crisis right now.

IMHO the problem is their yearly release cycle. Right now the feature might be too incomplete to include, which is fair. But in a few months it would be, but its still 10 months at minimum before Safari adds support for it.

Can you cite some examples?