The chance of looting a rare item from a boss with the reward system is higher alone or with a friend?
I have some official responses I'd like to quote about some bosses with the reward system but to sum it up: the chance of dropping an item on your character is not affected by a team or a solo kill as long as you met the required participation rate. The participation levels for each boss can be different when it comes to the reward system. We do not know all the details but this is the information and examples we're given. I do not have personal experiences or specific instances for each boss.
Participation levels depend on multiple factors for one the boss but also being active in a fight by dealing damage, or you block and thereby receive damage, or you support other members of the fighting team with healing (but just healing doesn't count, you need to do damage during the fight as well) (Source) and (Source)
"Keep in mind that there are different mechanics for different bosses. Let's concentrate on Oberon and assume, every player meets the participation requirements: The chance of looting an item as a team is of course higher than looting an item as an individual since all team members have a chance to loot one. However, the chance of looting one on your own character does not differ. Let's say there is a 1% chance to drop item X. If you go in alone or as a team does not affect this 1% chance. However, if you go in as a team of e.g. 5 people, all five of you have a 1% chance to get that item. So the overall chance that this item will drop for one of you is of course higher (5 x 1%). Yet, the chance that it drops for your own character remains the same. A unique drop means a specific item can drop only for one participant of the kill item." (Official CM Response)
Q: Which has a bigger chance to drop items from the final falcon boss? Doing it solo or as a team of 5? I mean everyone from the team has a chance to drop an item so 5x chances? If I made it solo it will have a 1x chance or the chances of the whole team "5x"?
A: The chances are the same for everyone as long as you meet the required participation rate. Therefore, the chance of dropping an item on your character is not affected by a team or a solo kill. (Official CM Response)
Items like Ferumbras' hat with a 100% drop chance will still drop only ONCE. Among all players who reached a certain participation level, ONLY ONE will get the hat. Other rare items will stay rare. For example: if ten players reach a certain participation level then all ten have the same chance to receive a great shield but only one will get it. Still, that is still only a chance and there is no guarantee the anyone will get the shield. So, rares will stay rare. (Official CM Response)
Some rares can drop for more than one player of course-
Q: Does this mean that it is possible for more than 1 character in the team killing the boss, to obtain a Falcon item?
A: Yes, given the rarity of the items it is not very likely but it is possible. (Official CM Response)