When to favor ng-if vs. ng-show/ng-hide?

Depends on your use case but to summarise the difference:

1. ng-if will remove elements from DOM. This means that all your handlers or anything else attached to those elements will be lost. For example, if you bound a click handler to one of child elements, when ng-if evaluates to false, that element will be removed from DOM and your click handler will not work any more, even after ng-if later evaluates to true and displays the element. You will need to reattach the handler.
2. ng-show/ng-hide does not remove the elements from DOM. It uses CSS styles to hide/show elements (note: you might need to add your own classes). This way your handlers that were attached to children will not be lost.
3. ng-if creates a child scope while ng-show/ng-hide does not

Elements that are not in the DOM have less performance impact and your web app might appear to be faster when using ng-if compared to ng-show/ng-hide. In my experience, the difference is negligible. Animations are possible when using both ng-show/ng-hide and ng-if, with examples for both in the Angular documentation.

Ultimately, the question you need to answer is whether you can remove element from DOM or not?

See here for a CodePen that demonstrates the difference in how ng-if/ng-show work, DOM-wise.

@markovuksanovic has answered the question well. But I'd come at it from another perspective: I'd always use ng-if and get those elements out of DOM, unless:

1. you for some reason need the data-bindings and $watch-es on your elements to remain active while they're invisible. Forms might be a good case for this, if you want to be able to check validity on inputs that aren't currently visible, in order to determine whether the whole form is valid.
2. You're using some really elaborate stateful logic with conditional event handlers, as mentioned above. That said, if you find yourself manually attaching and detaching handlers, such that you're losing important state when you use ng-if, ask yourself whether that state would be better represented in a data model, and the handlers applied conditionally by directives whenever the element is rendered. Put another way, the presence/absence of handlers is a form of state data. Get that data out of the DOM, and into a model. The presence/absence of the handlers should be determined by the data, and thus easy to recreate.

Angular is written really well. It's fast, considering what it does. But what it does is a whole bunch of magic that makes hard things (like 2-way data-binding) look trivially easy. Making all those things look easy entails some performance overhead. You might be shocked to realize how many hundreds or thousands of times a setter function gets evaluated during the $digest cycle on a hunk of DOM that nobody's even looking at. And then you realize you've got dozens or hundreds of invisible elements all doing the same thing...

Desktops may indeed be powerful enough to render most JS execution-speed issues moot. But if you're developing for mobile, using ng-if whenever humanly possible should be a no-brainer. JS speed still matters on mobile processors. Using ng-if is a very easy way to get potentially-significant optimization at very, very low cost.

From my experience:

1) If your page has a toggle that uses ng-if/ng-show to show/hide something, ng-if causes more of a browser delay (slower). For example: if you have a button used to toggle between two views, ng-show seems to be faster.

2) ng-if will create/destroy scope when it evaluates to true/false. If you have a controller attached to the ng-if, that controller code will get executed every time the ng-if evaluates to true. If you are using ng-show, the controller code only gets executed once. So if you have a button that toggles between multiple views, using ng-if and ng-show would make a huge difference in how you write your controller code.