Q: Should we set up a Facebook page of a Facebook group for our company/ organization /team?
If you are looking to move your brand into the world of social media, you will want to consider what kind of interaction you want with your supporters.
A Facebook Page is mainly used to allow your organization to more formally manage its push of information to the masses. Pages allow you track how many members you have and keep detailed analytics on page visits. It also allows for more targeted messaging. If you are going to be passing information from your organization to the public without much interaction with your members, you can use a page to brand yourself in the social media. You will most likely also want a Twitter and/or Google+ account for the same entity.
A Facebook group is more like an informal conference room with a less controlled environment. Everyone is allowed to talk and interact more freely, maybe even with different sub-topics of the original group. The group is more open to mass communications between the members and not just to the branded entity. Information in a group is usually more free-flowing than on a page. A group can also limit its membership by only accepting private members or requiring all post to be approved by an administrator before being posted.
If you compare it to live events: a page would probably have a speaker in formal setting and a group would be more of an informal meeting hall with maybe a presenter or two with free-flowing topics. Groups have the option of allowing everyone to speak while pages limit that ability but allow you to track visitors and analytics.