the biggest thing i've seen thus far that i find useful is the breakdown of heart rate zone data. here is an example of the reading from my most recent run.
(sorry in advance for the large size of these images, i wanted to make it 1:1 with how it appears in my browser.)
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garmin has this as well if you have a vivofit 3 or better device. i have found these two analyses can sometimes vary pretty wildly. strava's seems to be more consistent and is somewhat more user friendly, particularly on the mobile app.
here's the pace analysis. again, it's a slightly more robust version of what you get for free with garmin.
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and here is the pace distribution analysis. i don't think there is an equivalent of this on garmin connect, at least not for the vivofit 3 or under.
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for the most part, as i have mentioned, a lot of this is either already available via garmin connect or, possible, way too granular for most casual runners. i have not had any luck creating segments, which is a pretty big draw for getting premium. no have i poked around the training plan options.