When comparing Strava vs MAPS.ME, the Slant community recommends MAPS.ME for most people. In the question“What is the best gps app for bicyclists for navigating on iOS?” MAPS.ME is ranked 2nd while Strava is ranked 3rd. The most important reason people chose MAPS.ME is:
That saves a lot of download, e.g. from ~500MB in other applications it is reduced to ~50MB for German surroundings.
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Pros
Pro Keeps track of segments without user manually timing them
Segments - can track your improvements or compare with friends, club members without manual input. Or you can keep them private.
Pro Accurate distance measurements
Pro Allows challenging other people
You can set a goal and challenge friends as well as local professional athletes.
Pro Can share running routes with others
Running is boring if it's the same stretch of road. Stava lets you share good places to run.
Pro Supports multiple devices
Current list includes:
iPhone 3GS and later,
Android 2.2 and later,
Garmin Forerunner and Edge,
Soleus,
Timex Run Trainer 2.0
Pro Equipment tracking
This lets you figure out how many miles you've put on a pair of shoes before it's time to get a replacement pair.
Pro Watch the pros
You are able to follow some professional athletes and see their training etc.. Makes you realize how hard they train.
Pro Tracks heart rate with chest strap
Can also track heart rate with other types of HR monitors e.g. arm strap or smart watch.
Pro Very detailed selection of areas to download
That saves a lot of download, e.g. from ~500MB in other applications it is reduced to ~50MB for German surroundings.

Pro Includes offline routing and turn-by-turn navigation
Users without a data connection can still use the app for turn by turn directions, which is great for those that travel or use a device that does not have a cellular data connection.
Pro Obtains data from community-based OpenStreetMap
MAPS.ME uses data from OpenStreetMap, meaning the data retrieved from that service is a community-based map. Anyone can freely edit and contribute to the map, a map concept that is similar to Wikipedia.
Pro Fast rendering
By using compression of the map data, MAPS.ME is able to speed up the rendering of their maps to one's device. This allows for a quicker feeling app.
Pro Optionally can download traffic information
And showing it color-coded (Google-maps-like) on the streets.
Pro Discover nearby feature
Shows a nicely organize list of interesting places to visit close to your current location.

Pro Matching modern material-like interface
The design of the app uses a material-like interface making for a close to native looking experience on Android.
Pro Offline vector maps
Automatically downloads vector maps for offline use.
Pro No nagging advertisements
Pro Easy to install
Pro Easy adding/editing of bookmarks/favorite places
Click on the map and you will have the option to Bookmark, Route From, Route To. Having selected Bookmark simply offers to edit it, e.g. give it a different name.
Pro Allows to edit OpenStreetMap data
It is possible to add new and edit existing POIs in OpenStreetMap database using a nice interface.
Pro Night mode
There is a night mode option.
Pro Integration with booking.com
Displays information from booking.com about hotels and apartments.
Cons
Con Not for indoor spinning or gym workouts
Con No interval training!!!
Con By default, all your GPS data is made public
From their blog:
"The basic level is to choose to not use any privacy controls and make your info available publicly..."
Con Poor response time to recalculate the route
Con No option for satellite/aerial/topographic imagery
Not as useful for navigating while hiking/climbing/etc.
Con Very slow search and route calculation
Probably because MAPS.ME has more POIs in its database which ends up with all searches and route calculations being very slow.
Con No display of speed limit
Neither the next nor the current one.
Con No way to distinguish between fastest, efficient or shortest route
Con Very limited options
E.g. no way to hide certain buttons like the traffic button, or to configure the language used to display city names.
Con Sometimes very strange suggestions
E.g. when not using the suggested route, Maps&Me continues to request to turn even if you are more than 100m after the cross-road.
Con Favorites are a little bit too hidden
Because they are stored in groups.
Con Traffic information is not available in all countries and cities
Source of traffic info is a trade secret this feature is only available to some selected cities.
Con No lane assist
Con Being based on OpenStreetMap data can be lacking
The use of OSM also has the drawback of many places not getting the attention needed for updates. Depending on the geographic location OSM may have the most detailed maps or the most bare/outdated map.
Con Does not show images offline
Does not show images offline if supplied in standard kmz file. i.e. zipped kml plus image folder.
Con No tourist detail maps
