I've found that typically, most people think "if" sounds better, most of the time.
If you're going to make a mistake, you'll accidentally use
if where you should use whether. I very rarely see people use
whether where they should use if. For instance, this is the type of mistake I actually see (both on the GMAT and in real life):
"I wonder if she's going to the party?" (wrong - should be 'I wonder whether she's going')
I never see people make mistakes like this one:
"I'm not going to the party whether she goes." (wrong - should be 'I'm not going to the party if she goes')
So, I'd recommend leaning towards using "whether" if you're not sure. If you
need to use 'if', your ear should tell you about it. Otherwise, if you think it's ambiguous and you're really not sure which one is right, 'whether' is usually the right choice. This rule of thumb will probably be easier to remember (and easier to use on test day) than trying to suss out the meaning of the sentence.