AJAX Polling Frequency - To long poll or not to long poll?

I'm building a component of a web page that needs relatively constant database polling. I can see two different approaches for this, and I'm wondering if one of them is better than the others, or if I'm missing a third option.

1) Send off an AJAX request every 1 or 2 seconds to check for updates. Each request returns immediately whether or not there is new data.
2) Fire off a single AJAX request that will not return until it receives data or a timeout occurs. Upon either of those happening, it fires off the next request. (I think this is called long polling?)

The number of database queries will be the same with either, but with #2 there would be fewer requests firing from the browser which could save bandwidth and client resources. For the server, is it better to have a single PHP request that stays active and sleeps between queries, or that fires up every few seconds, polls the DB, then shuts down? Or is there no difference and I'm stressing about this too much?

EDIT: I suppose I should also state that this is a chat widget of a larger web app. A slight delay in communication is not going to kill a user, as chat is a secondary feature.