What a group really gives you is a shared day of prayer and someone else carrying the logistics. Many groups travel with a priest, which is how a daily Mass at the shrines is arranged; ask whether one is coming instead of assuming it. A guide explains what you are looking at, the coach is waiting, and the reservations that are hard to get have been requested months earlier. What you give up is control: fixed mornings, a group pace, and less room to stay somewhere that moves you.
Traveling independently, you keep that freedom and take on the work. Some visits must be requested well ahead: the Scavi tour to the tomb of St. Peter is booked only through the basilica’s Excavations Office, in groups of at most twelve, with advance booking required and no children under 10. Other things cost nothing and need no organizer: tickets for the Pope’s general audience are always free and are requested directly from the Prefecture of the Papal Household. On the Camino de Santiago, anyone who walks the required distance receives the Compostela, with a group or alone.
Before you choose, ask an organizer four things: whether a priest travels with the group, how many times you change hotels, how far you walk each day, and what is not included. If you would rather go alone but worry about a first visit, a middle way works well: travel independently and book a local guide for the one or two days where explanation matters most.