Looking at your picture, you have a very limited space to turn that fitting.
I am going to guess that your thread is leaking because it is not tight enough which means switching to a Sharkbite may not help as you will also need to thread this on.
Which every fitting you decide to go with, I would make sure that:
1. Teflon tape is wrapped around the pipe 3-4 times. You need to make sure the direction of the tape is clockwise (same direction as the fitting that will be screwed on)
2. As the previous poster said, apply some pipe dope on top of the Teflon tape (once again, applying it in the same direction)
3. Turn the fitting until is tight with a medium sized wrench, then turn extra 1/4 (no need to go Superman on that fitting).
Thanks. I "thought" I had tightened it enough. I had 4 wraps of Teflon tape on clockwise and tightened them all down while holding the valve in my hand until I couldn't tighten it anymore. I will try the pipe dope and I guess try to put more muscle into it. I was afraid of over tightening previously.