There is no best pattern, only the one whose trade-offs suit the work and the people. The numbers below are computed from the patterns themselves (crew A, 12-hour shifts except the fire-service patterns), so you can compare like with like before a roster change is proposed or accepted.
Pattern
Hours / week
Most in any 7 days
Days off / yr
Full weekends off / yr
Longest run
Longest break
2-2-3 (Pitman)
42
60
183
26
3
3
4-on-4-off
42
48
183
20
4
4
3-on-3-off
42
48
183
17
3
3
DuPont (28-day)
42
72
183
26
4
7
24 on / 48 off
56
72
243
17
1
2
48 on / 96 off
56
72
243
26
2
4
What the numbers say
All the 12-hour patterns average 42 hours a week and 183 days off. The difference is how those days are arranged, not how many there are.
Pitman never has more than three shifts in a row and gives every other weekend off, but a 3-shift block and a 2-shift block either side of a short break make a 5-shift (60-hour) week. It is popular because the breaks are short and frequent.
4-on-4-off has the gentlest worst week (4 shifts, 48 hours) but fewer full weekends off, and a four-night block is a long run to stay alert through.
DuPont has the longest break, seven days every four weeks, paid for with a 6-shifts-in-7-days stretch (72 hours) when it switches between days and nights.
24/48 and 48/96 have the most days off, and the highest hours on the clock, which is why fire services treat their hours differently from 12-hour shift work.
Questions to ask before you switch
What is the worst 7-day stretch, and how is overtime defined for it where you work?
How many consecutive night shifts, and how long to recover after them?
Do the same people end up on weekends, holidays or the night crew forever?
How does handover work when a crew changes mid-pattern?
Using the generator
Choose your pattern in the tool, see your crew's calendar and download it as a calendar file. If you do not know which crew you are, enter a few dates you remember working and it finds the crew and cycle day for you.