Does the second round of reviewing process typically take a longer time than first round?

In my experience, it is usually the other way around. The first round of reviews typically takes longer, because the reviewers are new to the paper and first reading it and forming their opinions. In the second round, they are more likely to be simply looking at differences and seeing whether they agree with your adjustments and replies to their comments.

There is, however, a lot of noise in the process, because in most cases the main amount of time is not spent in reviewing per se, but rather in waiting for the reviewers to make time in their schedules to review. It differs from journal to journal of course, but sounds to me like in your first round of review you got unusually lucky with the reviewers' schedules and things went very fast, and the second round of review is taking a more "normal" length of time.

To add to jakebeal's answer, the second (and later) rounds of reviewing are usually faster not just because the reviewers have already seen the paper, but also because the reviewers are less likely to not submit a review. A lot of the variance in the time taken is because reviewers decline to review, do not submit a review by the deadline, and so on, which forces the editors to invite new reviewers and start the clock from scratch. But after they've already reviewed a paper once they are more likely to agree to review again as well as submit a review before the deadline.

Also, many of the journals I've seen have set things up so that the deadline for the first round of review is slightly longer than the deadline for the second and further rounds - by about 25%.