Using a Cateye Strada Smart and Strava
First rule of on-line bike ride tracking... every single one has secret-sauce that they use to tweak your ride data.

Strava ignores height information and simply plots your path's point locations on top of a map and that's how high you were.  This method is pretty flawed if your GPS has placed you 20 metres off the road and you're in a deep cutting or on the side of a mountain with a hundred metre vertical drop to that side.

I don't know anything about the Cateye services.

The only answer is to take their results with a big pinch of salt, and merely work on improving the difference between the rides.  Don't compare rides between different providers.