I agree with cmaffia's response and want to add a few more points. As he stated, this is first about tone, and that is affected by the amp and speaker you run through, the room and its furnishings, the position of the speaker(s) in the room, and the position of the recording mic on the speaker cabinet — they will all affect that. My experience is that recording direct has never given me a sound that I like.
However, if you ever want to change or remove an effect or want to edit your guitar take after the fact, such as with a tool like Melodyne, then you want the signal as clean and pure as possible. As soon as you begin to add any effects to a guitar's output, especially grunge or outright distortion, the additional artifacts will become almost impossible to edit properly and the result will be cruddy. So I like to record the guitar output directly as well as from miking the amp itself. The direct take allows you to re-amp the sound later. That means that you can edit the guitar take, or even just change the effects in the guitar chain, both pedals and any effects contained in the amp itself, without having to record another take of you trying to play the part better or identically.
To re-amp a cleanly recorded guitar, take the output of the cleanly-recorded track, run it through a re-amping box (some direct-in boxes can include this facility) and into any pedals, then into the amp of your choice, and finally into the speaker cabinet(s) of your choice. The foregoing gives you almost any option you can imagine to re-color your sound using any effect (or combinations of effects), amplifier, and speaker cabinets just as if you played the edited take perfectly through the new combination. The re-amping box provides proper impedance matching between the low impedance output of your interface and the very high input impedance of the typical guitar pedal and/or amplifier.
