PageSpeed is the biggest thing that is available in IE that you can't get from any of the other browsers but it's a fairly old version of the checks at this point and doesn't remotely match what the online Page Speed Insights tool checks.
With Chrome we could also get some stats from the timeline (amount of time spent running javascript for example).
Both IE 11 and Chrome would let us measure the adoption of SPDY/HTTP2, Newer image formats (webp/jpegxr).
Being able to trend historically is going to be a really big problem though and not just with the initial transition. Chrome updating every 6 weeks will change the results in ways that may not represent changes in the sites (though it will reflect how users are consuming the sites). Even IE 11 pushes new functionality with Windows Update these days though the changes are probably not going to be as large as what you will see with Chrome.
When we make the transition we're definitely going to want to run both in parallel for a period (or at least a subset on the new browser) so we can test both the processing and what the impact on the stats is going to be. One thing we might be able to do is instead of always doing 3 runs we could configure it to do "up to X runs" until it gets a successful result which might buy us enough headroom to run both in parallel now.
My vote would be to transition to Chrome for desktop but to do it slowly (soon, before we ramp up to 1M URLs and cause even more headaches) and work through the "moving target" issues. When we have more capacity we can consider adding IE back (or even IE and Firefox).