I really thought we could upload videos here so I just used my prefered recorder. For some reason it rather bothers me that screencasts are just uploaded under community. I assume they aren't publicaly visible without a shared link but it still makes me uneasy thinking of them being public. Not so much these videos in particular but just in general.
I tried your suggestions and it didn't make any difference. Here are the examples.
Here is freecad.
Now you can see when I grab the screen in the middle left and drag horizontally the behaviour is different than if I grab at the top left and drag horizontal. If I grab in the top center and drag vertically the motion will be different than when I grab the top left and drag vertically.
Next I position the flange at a diagnol and try to lay it down more on it's face. By grabing in the right spot it rotates easily on the desired axis.
Next note how easy it is to square the part back up at the end. I know this isn't necessary in F360 as you can just select square views but notice how much dexterity I have in moving it exactly how I want by grabbing a different area of the screen and that changing the motion on the part.
And lastly look at how consistent a corner to corner drag is giving a very predictable rotation and putting it back where it started when I return.
https://knowledge.autodesk.com/community/screencast/1006d75f-4c71-45a6-b0d4-61f4db6b288c
Now F360.
Whether I grab the left center of the screen or the left top of the screen and drag horizontally the effect is essentially the same although at the top it definitely seems a little unstable and jittery. If I grab the far left upper corner and drag down the effect is the same as if I grabbed it in the center and dragged down.
The diagnol drag is the one place where the mouses location on the screen seems to have some effect but not in a desireable way. As the mouse gets closer to the center the motion becomes very unstable and unpredictable. Because of this when I drag the mouse back to the same point on the screen the part is in a different position. That is not an issue in it's self but it shows how unstable it seems to be.
The next part is the issue that I have had on a regular basis. This happens all the time when I am trying to get the perfect angle for a render but even sometimes when I am trying to get the part so I can see into a tight corner or hard to see spot i can bat around at the model for ages and never find the right way to get it where I want it.
Getting it to the diagnal position is easy enough but from there I want to tip the face downward just as I did in freecad. I could have done this much better in freecad if I were in practice but I got it decent pretty quick. In f360 however there is no motion to make this happen.
It's like if Freecad uses your hands to position the part F360 uses a pool noodle duct taped to a baseball bat to position the part.
https://knowledge.autodesk.com/community/screencast/1d34e945-0ba3-4e8b-b8fd-7d41a835240a
https://www.facebook.com/groups/1229995573786339/