I would prefer better load times in Analytics. It samples the actual load time of the pages on your site, and is a good indication on how fast your users are seeing your content. You build your site for users, not for search engines. Normally, the faster your site loads, the better the user experience will be.
Apart from that, Analytics allows you to analyse which browsers, operating systems, etc. have the best/worst loading times, which helps you to prioritise the issues that should be solved.
Page speed insights is a great tool and will give you a lot of useful information on how you can optimise. It's is not a measure of how fast a page is loading. If you have 4 x 200KB images on your site, that are losslessly compressed - the tool will be quite happy to give you a good score on image optimisation, even if images of this size will take ages to load over a mobile connection. On the other hand, it can give you a low score for some render blocking javascript or css file, that in reality hardly has an effect on the user experience.
There is a 3rd tool I often use to measure pagespeed (webpagetest.org) - it also indicates areas of improvement and gives scores on each individual item, and it will also shows you the load time of each individual item on your page. Maybe most important feature: it allows you to see how fast the visible content is completely rendered on screen (which is in fact the most important measure for your visitors).
Hope this helps,
Dirk