The mishna is speaking on a halachic basis and not on the actual length. That is, we follow the same halachos except that Taanis Esther and Purim are pushed to the second Adar (which was the original month) in order to be close to Pesach.
What I meant was the usage of ain bain in the mishnah as expressed talks about the halachos of the month and does not deal with the length of the month. Technically, the length of every month can be either 29 or 30 days based on when the witnesses arrive at the Sanhedrin. The fact that the fixed calendar was set up later is a separate matter and based on mathematics and designed to make the minimal change at the latest time possible in the year.
The basic lunar cycle is 29.5 days (plus a fraction - 44 minutes + 1/1080 of an hour called a cheilek). As a result, the lunar year should (approximately) alternate 29 and 30 day months. The lunar year is therefore 353, 354, or 355 days long as opposed to the 365.25 day solar year. Since the difference builds up to a full month after three years, an extra month needs to be added to the year. In order to make up the difference, and keep the relative new moon position (and keep Pesach after the spring equinox) we need to "round up" the 29.5 days to 30 days. This therefore makes a leap year 383, 384, and 385 days so that the net number of days over the 19 year cycle comes out even (lunar and solar). There are 7 leap years in a 19 year cycle. Had the intercalary month been 29 days, the 19 year cycle would have lost a full week and would have continued to get out of sync.
The 19 year cycle is actually not quite completely accurate because the solar leap year is not rigidly every four years. Those "century years" which are not divisible by 400 are not leap year (no February 28) according to the Gregorian calendar (such as 1900). As a result, Pesach has been getting "later" in the solar year as the centuries go on. Eventually, the Sanhedrin will have to "skip" a leap year when the current fixed calendar says it should be one and make it the next year. I discuss this and the reasoning behind it at What will happen to the calendar if the Sanhedrin is re-instituted. Of course the necessity for this is not for a long time and the Mashiach will have come before that happens, so the Sanhedrin will have been established and we will no longer be on the fixed calendar.