macOS Cmd-Tab Overlay – How to Disable Mouse Interference

control+F4. Cycles through the applications in that Space.
(I actually have this mapped to control+`; which I find easier to remember, being close to the cmd+`; to cycle through an application's windows.)

To change the keyboard shortcut, go to the Keyboard preferences, Keyboard Shortcuts, and Keyboard & Text Input. It's the 'Move focus to active or next window' option.

(Edit to fix the keyboard shortcuts; I didn't realise that the backtick character wasn't showing up.)

It seems like what you are referring to is not a problem with your mouse (as you've tried several). I'll also rule out the silly possibility that you are using all those mouses on a sub-optimal surface, like glass or uneven and rough wood, etc. I think you're simply experiencing the effect of different mouse acceleration algorithms between different operating systems.

As the physical hand/mouse movement cannot practically be mapped 1:1 to the cursor movement (you'd need a trackpad as big as the screen!), some kind of mapping algorithm between the hand movement and cursor movement is necessary. Mac by default implements it so that slow hand movement maps to a very slow cursor movement (for precise targeting), and a relatively fast hand movement maps to a very fast cursor movement (for moving quickly in a general direction but without fine-level accuracy). On Win machines a bit of this kind of acceleration also exists but it is not nearly as pronounced as it is in OS X. Some Win users switching to a Mac might find this maddening as their muscles and motor skills are used to something different. But same is true for a Mac user switching to Win. I.e. a Mac user might feel that mouse is traveling way to slow when reaching distant parts of the screen, and it's harder to do fine targeting in a small area. The Mac way does seem to work better the larger the displays are since it's benefits are more obvious in that case.

The good news is that if you just give it a week or two of constant usage, your muscles will likely get used to it and you won't perceive a problem at all. Based on your description, you might want to increase you mouse speed a bit though, to split the difference between big broad moves, and tiny, precise ones.

As a last resort, there are apps like Controller Mate: http://www.orderedbytes.com/controllermate/help/?show=configaccel that let you adjust the acceleration algorithm used yourself.