Matthew 6.1- 8
Beware of practicing your piety before men in order to be seen by them; for then you will have no reward from your Father in the Heavens.
Thus when you give alms, don't sound a trumpet before you, as the hypocrites do in the synagogues and the streets, that they may be praised by men. Truly I say to you, they've received their reward. But when you give alms, do not let your left hand know what your right hand is doing, so that your alms may be in secret; so [only] your Father who sees in secret will reward you.
And when you pray, you must not be like the hypocrites, for they love to stand and pray in the synagogues and at the street corners, so they may be seen by men. Truly I say to you, they've received their reward. When you pray, go into your room and shut the door to pray to your Father who is in secret; and your Father, who sees in secret, will reward you.
In praying, do not heap up empty phrases as the Gentiles do, thinking they will be heard better if they use many words. Don't be like them, for your Father knows what you need before you ask Him.
In Rabbinic Judaism they make the same distinction, except that they do consider a public gift for personal glory to be better than no donation at all.
Quakers may make too much of a virtue of such reticence, in that often you don't find out what a Friend has been doing until they've died and stopped doing it.
Especially in the case of prayer, I would rather hear it more often -- because I've only known one occasion when one of the older members prayed in Meeting; and by that point the group had wandered far into despair over the crummy State of the World. It isn't so much that we'd need some person to 'lead us in prayer' as that we really need to know there's at least one person present knows the presence of God and knows Who to petition for redress. Great length, putting words in our mouths (or God's) is a flaw, but so is lack of faith. Prayer, like any Message, would need to be something a person is moved by God to say -- but the example and the expectation that we can potentially be inspired to this might help a lot sometimes.