I've been using both in parallel for quite a time and am now solely using runalyze. Not only because I quit using Garmin products, but also because I never trusted Garmin's metrics. In comparison, runalyze was always spot on with predictions and such. Also, the user interface is something I like a lot more. Remember the bad pace charts etc. in Garmin with no real scale options, and such.
My last marathon (2018) was predicted by runalyze on the minute. Garmin's predictions were way off and also had a lot of errors that could have been fixed by simple sanity checks. For instance, I had a determined threshold pace and the race predictor predicted a time that was faster as my threshold pace for the marathon distance. Absurd.
Also, not sure if this is still valid, Garmin did only account workouts recorded with their devices into their metrics (due to license issues). Not good if one is using other devices too, like I do, e.g. Zwift.
Overall: I see no point in using Garmin Connect over runalyze, it is way ahead in terms of analysis features for sports people. Sure it has less social features or route creation, but there are better other tools for that.
The developers are true sports men and are very responsive when one has questions or there is a bug.
Give it a try!