I think Strava is much better than it was.

I've had it actually running, and ticking up time, but not counting mileage, but it hasn't done that for over a year now.

Different systems are different.

With RideWithGPS, to "pause", you must hold the button down.
With Strava, they use a circle to start and a circle to stop, and just touching it, and everything stops.

I use the Strava mapping mode a bit, and have not immediately realized that a moving dot means that it is not recording, while a TRON-like line behind me means it is recording (if I'm using a route, then I will be following a line).

I use the button on the bottom of my phone a lot to wake it up and swap between applications. But, it is also imperceptibly below the STOP button on Strava.

RideWithGPS has "handlebar" mode which is nice. So, it will activate over the top of the greeting screen.

However, if I'm wanting to run Strava or RideWithGPS while not looking at it, then I try to background the applications, so it takes multiple button presses to get back to it (less likely to be bumped).