Best apps for running

I'd start with suggesting that a Fitbit isn't the right tool if you want to be able to map your running, so I'd be aiming for a Garmin.

Notwithstanding that, I've used Endomondo, Runkeeper, Strava, Runtastic and MapMyFitness. My observations would be, in order of recommendation:

Endomondo - Probably my preferred app. I use the training plans feature in premium, for 10Km, Half Marathon and then Marathon, both completion and speed improvement plans. The tracking is solid, although the calorie estimations are a bit high. Good integrations and analysis.

Strava - Very reliable with a good web service backing it up. Powerful analysis and the ability to compete segments against others is useful for the more advanced trainer.

Runkeeper - Reliable, pretty consistent with a decent community functionality. Fewer integrations and the analysis tools aren't great.

Runtastic - Naggy upselling, battery hog, but when it worked it was good. Very cluttered website.

MapMyFitness (MapMyRun/ MapMyRide etc) - I had consistent problems uploading and find the website very cluttered and ugly. Others love it.

Note if you do get a Gamin it can automatically transfer the files to MFP, Strava and Endomondo.

I use a Forerunner 310XT, it's now quite an old design but I picked it up for £120

I have the Fitbit Charge HR and am a runner-you'll still want the apps for the GPS of tracking miles, routes, etc. the Fitbit is only for tracking daily steps. I also have a Garmin I picked up on Amazon for about $120. It's a older model but is the only thing I use when race training.

Apps I use are Nike and MapMyRun. I've been having issues with pacing on the latter and calories are way too highly calculated. But for my everyday runs, it's fine.

I'm also a fan of Endomondo, but for different reasons.

I use a Garmin forerunner and it syncs with Endomondo. Endomondo uses Garmin data as Garmin sends it. Unlike Strava it does not apply its own calorie estimation or auto-pause. It pulls the data exactly as Garmin has. Also it tracks any split of x distance as a potential Personal Best. So say while I don't necessarily race 5ks, it'll track your fastest 5k split and you can see a graph of your fastest 5k split over time (days, weeks, months, years). It's a good way to track personal fitness, because if you are improving you should see that 5k split go down over time. Strava & other apps try to do this, but sometimes don't pick every run equal to or greater than 5k and give you comparison of every fastest split. Time based splits like Copper (12 minute) & 1 Hour also equate well to MaxVO2 & Aerobic capacity. If you are improving you should be able to cover more distance in a 12 minute period or over the course of an hour.

I still use other services like Strava (social & pace distribution based on previous race), Garmin Connect (serves data to other services, review interval splits that aren't equal to a mile, create interval workouts to send to GPS watch) & Smashrun (layout & unique metrics) but the above aspects of Endomondo are why I tend to like it more.