Prayer, private and public
Drawing on some quotations from the Urantia Papers
"Jesus taught the twelve always to pray in secret; to go off by themselves amidst the quiet surroundings of nature or to go in their rooms and shut the doors when they engaged in prayer." [UP144 §3 ¶14] Jesus himself "went out in the hills to pray so many times because there were no private rooms suitable for his personal devotions." [UP145 §5 ¶2] We are instructed to keep personal devotions private.
Jesus said to the apostles: "…when you pray, go apart by yourselves and use not vain repetitions and meaningless phrases." And "…be not given to fasting with a sad countenance to be seen by men." [UP140 §6 ¶11] Obviously, the self-vaunting kind of public praying (or braying) is what's disapproved here.
Jesus "did not fully approve of the practice of uttering set and formal prayers" [UP144 §1 ¶10] and a Brilliant Evening Star likewise decries that even today "You address one another in common, everyday language, but when you engage in prayer, you resort to the older style of another generation, the so-called solemn style" [UP87 §6 ¶14]. Jesus "rarely uttered his prayers as spoken words. Practically all of Jesus' praying was done in the spirit and in the heart — silently." [UP144 §4 ¶10] Such informality and spirituality is more characteristic of personal communion than group prayer.
"But prayer need not always be individual. Group or congregational praying is very effective in that it is highly socializing in its repercussions. When a group engages in community prayer for moral enhancement and spiritual uplift, such devotions are reactive upon the individuals composing the group; they are all made better because of such participation. Even a whole city or an entire nation can be helped by such prayer devotions. Confession, repentance, and prayer have led individuals, cities, nations, and whole races to mighty efforts of reform and courageous deeds of valourous achievement." [UP91 §5 ¶2]
Them's mighty potent words, eh? Moreover, "There is a certain danger associated with overmuch private praying which is corrected and prevented by group praying, community devotions." [UP91 §7 ¶13] As he was about to resurrect his friend Lazarus from the dead, Jesus prayed aloud, and if that wasn't for some good effect upon those at hand who were grieving, then why do it? Jesus prayed, "because of those who stand here with me, I thus speak with you, that they may believe…." [UP168 §2 ¶2]
Point 11 in a list of points Jesus emphasized at Jotapata includes this: "Let your real petitions always be in secret. Do not let men hear your personal prayers. Prayers of thanksgiving are appropriate for groups of worshipers, but the prayer of the soul is a personal matter. There is but one form of prayer which is appropriate for all God's children, and that is, 'Nevertheless, your will be done.'" [UP146 §2 ¶12] So there's the difference between personal and public praying.
Group prayer, that is to say group petition as opposed to prayers of thanksgiving, would seem to be for group or community purposes, or for those things beyond the individual's ability. At any rate, prayer "has been wrongly emphasized by modern religions, much to the neglect of the more essential communion of worship. The reflective powers of the mind are deepened and broadened by worship. Prayer may enrich the life, but worship illuminates destiny." [UP102 §4 ¶5]
"In the old order you fasted and prayed;
as the new creature of the rebirth of the spirit,
you are taught to believe and rejoice."
—Jesus [UP143 §2 ¶3]