Recording to a click
Recording to a click seems to be the default choice these days and it definitely makes a lot of sense. It allows you to work with loops, copy and paste different parts of the arrangement (for example a verse or a chorus), synchronize your effects (delays, LFO etc) to the tempo of the session and in general I would say that it is a much faster way of doing things.
This method might be extremely effective but every now and then I also find it a bit limiting and end up recording without a click. Recording without a click allows you to randomly speed up and slow down which makes the song more dynamic and adds a feeling of movement. I also find that sometimes focusing on the click can distract you from hearing your instrument and from my experience some musicians actually play much better and tend to improvise more without a click.