Have at You!!!!!
One of the huge changes to 6th is the challenge mechanic. To begin with the following units can make/receive challenges from the Tyranid codex. Broodlord, Hive Tyrant, Tervigon, Parasite of Mortrex and Tyranid Prime.
The first thing you should know is that single model units must accept challenges, that’s the Hive Tyrant and Tervigon.
If you opponent doesn’t challenge you can challenge him, even if its his turn.
Challenges continue until one side breaks or one of the two models in the challenge die.
For every 5 models locked into combat with a challenge (and therefore watching the challenge) their character gets one re roll (can be to hit, wound, or saves) this would mean that Feel No Pain could not be re rolled since that USR specifically says it is not a save. Unless you have the Parasite or a Tyranid Prime in a Challenge you will not benefit from this rule but your opponent likely will.
There are no clear rules on what happens if a different unit assaults the bystanders in a challenge so you may want to work that out with your opponent ahead of time, I lean toward allowing the additional assault to happen, meaning you and they get to swing while the challenge also continues.
When is it favorable to challenge?
Well if you assault into combat and don’t want to kill the entire unit its possible to use this mechanic to kill a character and stay in combat, this works best against fearless opponent.
When the rest of the unit has the ability to kill you. If your character is assaulted by TH/SS terminators challenge their Seargant, its silly for the marine player to accept, but he may.
When you really need to kill that one character in a unit, lets say the only character is their warlord and you need that VP, well challenge him if you can beat him, if not he will likely challenge you.
When is it not favorable to challenge/accept a challenge?
Unfortunately you often won’t have a choice since as I already meantioned most Tyranid characters are Single model units and must accept but one scenario that comes to mind: When your unit would likely do more damage to the opponent than the character, this could be say with a Broodlord and a large unit of genesteelers verses a unit of marines.
In the end Tyranids characters (even Tevigons with some Biomancy help) are really very good in close combat, so when you can get the most out of the challenge mechanic.