As of now, there isn’t enough research to make a consensus that one is better than the other. Based on human evolution and natural vitamin D production, it can be thought that daily intake is better than weekly.
This is because we evolved to receive sunlight everyday, as opposed to only going outside one day per week as is common today.
With supplementation, there is no concrete research to prove one is better than the other. While weekly dosing is likely to be okay, monthly or more infrequent dosing can make it more difficult to maintain levels in the healthy range.