An average of averages problem, or two valid results?
In you first approach you take into account the number of logins for each user, which you do not do in the second approach. Take the following example with two users with a different amount of logins:
$
u_1 = {7, 5, 10, 10, 8} \\
u_2 = {1}
$
Using the first approach the average would be 6.8 days whereas the second approach would give an average of 4.5 days. The second approach does not take into account that we have more observations for the first user (with a higher number of days between logins) than for the first user. Which approach is the best would depend on what question you are trying to answer, but I think generally the first approach would be more accurate in getting the average time between logins.