Javascript: What's more efficient, IF block or TRY/CATCH?

Exceptions should be used for exceptional circumstances (i.e. things that you don't expect to happen normally). You should not, in general, use exceptions to catch something that you can test for with an if statement.

Also, from what I understand, exceptions are much more expensive than if statements.

Use the if statement. I don't know what the overhead is for a TRY/CATCH, but I suspect it's far greater than evaluating a boolean expression. To hit the TRY/CATCH you will have to: execute a statement, generate an error [with that associated overhead], log the error (presumably), made a stacktrace(presumably), and moved back into the code. Additionally, if you have to debug code near those lines the real error could get obfuscated with what you are TRY/CATCHing.

Furthermore, it's a misuse of TRY/CATCH and can make your code that much harder to read. Suppose you do this for longer or more obfuscated cases? Where might your catch end up?

This is referred to as Exception handling

EDIT: As commented below, you only take the runtime performance hit if you actually cause an exception.

The other answers are correct, try/catch is for exceptional circumstances and error handling. if conditions are for program logic. "Which is faster?" is the wrong question.

A good rule of thumb, if you're doing nothing with the exception, it's probably not an exception!

To figure out which to use, let's break down your if condition.

1. typeof jQuery == 'function' Is the jQuery() function defined?
2. typeof nav == 'object' Does the nav global variable contain an object?
3. typeof pageid != 'undefined' Is the pageid global variable defined?
4. typeof document.getElementById('leftnav') == 'object' Does the document contain a leftnav element?

The first is clearly an exception. You ain't getting far without a jQuery() function.

The second is also an exception. You're not going anywhere without a nav object.

The third is an exception. You need a pageid to do anything.

The fourth is probably logic. "Only run this code if there is a leftnav element". It's hard to tell because the rest of the code doesn't reference a leftnav element! Only the comments do, a red flag. So it's probably a programming mistake.

So I'd probably do this (with apologies if I'm butchering jQuery):

var intvar = setInterval(function() {
    // If there's no leftnav element, don't do anything.
    if( typeof document.getElementById('leftnav') != 'object') {
        return;
    }

    try {
        clearInterval(intvar);
        jQuery('#'+nav[pageid].t1+'>a')
            .replaceWith(jQuery('<span>'+jQuery('#'+nav[pageid].t1+'>a').text()+'</span>'));

        //set display classes for nav
        jQuery('#'+nav[pageid].t1)
            .addClass('selected')
            .find('#'+nav[pageid].t2)
            .addClass('subselect');     //topnav
        jQuery('#'+nav[pageid].t3)
            .addClass('selected')
            .find('#'+nav[pageid].t4)
            .addClass('subselect');     //leftnav
    }
    catch(err) {
        ...do something with the error...
    }
},100);

...but I'd really examine if the leftnav element check is applicable.

Finally, I can't help but comment that this "function" is working with global variables. You should instead be passing nav and pageid into the function in order to maintain encapsulation and your sanity.