Dialog
"A dialog is a small window in which the user is prompted to make a decision or enter additional information. The dialog box does not fill the screen and is usually used for modal events that require users to take action before they can continue."
AlertDialog has many options, and as far as I can guess your problem, you can have a cross button in the upper right corner of the dialog box too (you can set icons anywhere since you can provide a custom layout for AlertDialog).
- Ability to add any kind
- easy to edit
- Can be adapted to tablets or mobile phones in landscape or portrait, just by changing the layout
-Can highlights a whole new class to change it in its path
Popup windows
"This class is a popup window that can be used to display an arbitrary view. A popup window is a floating container that appears on top of the current activity."
PopupWindow is another tool to customize your custom pop-up window anywhere on the screen. If you always show this popup in the middle of the screen, I would suggest not using it. AlertDialog should work fine.
-Simpler
-Easier for code
-It is more standard, so it will be difficult for the user to go astray with him
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