Axiom I do not think that the Steam controller and the Logitech F310 are even close to be comparable... It's like comparing a hammer and a saw... Two good tools, but not at all the same kind of tool!
To me, your Logitech F310 compares to a dual shock controller. The Steam controller is made to compare with a mouse/keyboard combo...
I give you that for games optimized for dual shock-like controllers, the Steam controller does not bring much to the table... Where it shines, is in games where mouse and keyboard works wonders, but the relaxed "10 feet experience" is lacking because of the desktop PC...
So far, I've tried Portal I and II, Tomb Raider 2013 and Bioshock Infinite on both mouse/keyboard and the Steam controller and what I have found, is that it is much more enjoyable and ergonomic on the Steam controller... Button placement makes a lot more sense and Gyro for fine movements completes it fantastically. If something feels wrong, you just need to remap as you wish...
I also tried Grow Home and Rifter on an Xbox controller, a dual shock clone and an 8bitdo SNES PRO but none was as satisfactory as the Steam controller. The 8bitdo SNES PRO was the second best but gave me a lot of fatigue in the hands and thumbs because of the small travel offered by the joysticks. I can play for several hours on the Steam Controller and develop absolutely no fatigue...
I yet have to try it on Esports titles, like Overwatch, but since I rarely boot my computer in Windows anymore whenever I want to play this game, it has to update for one hour, then I have to re-learn it as all characters mechanics have changed! (And this game is barely playable in Linux, even with the latest DXVK and proton development)
So yes, The Steam controller has a steep learning curve, as it is so different from what we are accustomed to, but now that I've got the grasp of it, I can't go back to other style of controllers (except for NES/SNES games, where the SNES controller is my favorite option).