The main pro is of course that it cuts your lecture preparation time in half. Since for many courses lecture preparation is the most time-consuming aspect, this is a very significant time savings. That you don't know this already makes me suspect that your teaching responsibilities are rather light. At my institution, a full-time instructional faculty would teach four courses per semester (and at some other institutions it would be five). Even a tenure track faculty member at a nationally ranked liberal arts college will often be teaching three courses at once. In these circumstances it is common to speak of "preps" -- i.e., the number of distinct courses you're teaching. So e.g. an institution with a 4-4 teaching load, it might be a policy that an instructor never has more than two preps per semester.
I have taught a lot of freshman calculus myself, and after you get experienced enough the prep time really dwindles. For instance, if you're going to lecture on integration by parts, you decide that you will introduce the formula by anti-differentiating the product rule, then do a few examples showing various standard techniques, then go back and talk about definite integration, then do a few more examples. I could give that lecture right now and it would go fine. It would go better if I thought more carefully, but I think the quality would level off at about 20 minutes of preparation. You've taught the course enough times that you're probably in a similar situation. But even 20 minutes a lecture adds up. Also, since freshman calculus is just about as minimally prep-intensive as it gets, teaching any other course would increase your prep time. And the non-lecture parts are still more efficient if it's two sections of exactly the same course. Presumably you're writing the exams, and I hope you're writing different exams, but writing two different sets of exams for the same course is still a lot easier than writing exams for two different courses.
As the other answer mentions, you do experience a bit of "Wait, did I say that five minutes ago or 75 minutes ago?" when you teach the same thing twice on the same day. It can feel a little weird...but it's not a problem. If discrepancies arise between the two courses, you had better write them down, because they will be very difficult to remember. You'll always be asking students which section they're in. And finally: yes, it will certainly be less interesting than teaching two different courses, but it sounds like you have plenty of other things to occupy your interest.
I want to end with some commentary. A calculus lecture with 300 students sounds rather outmoded to me. With that many students, there cannot be any reasonable expectation that you will stop to field many student questions: if 20% of the students asked a question, those questions and their answers would replace most or all of the lectures. You are also not grading their exams. Probably you're not holding office hours for 600 students in a meaningful way. So what teaching is really being done here? Is the only reason it's called two sections instead of one is because there's no room to seat 600 students? Are the students really getting more out of your lectures then if you just videotaped them and then they just played later to whoever wanted to see them?
I don't think this is a very good pedagogical choice. At my department we recently adopted a small class initative, in which all precalculus and calculus I courses are capped at 19 students. To cover all these courses we had to hire a ridiculous number of new instructional faculty, which frankly I worry could be bad for the long term health of the tenure track faculty. But as a pedagogical choice, it seems to be working very well. A "lecture" for 19 students is different thing entirely than a lecture for 300 students: the instructor really can interact individually with the majority of the students in a given class period. If you are long term member of your department, I respectfully suggest that you reconsider the practice of having such large lectures.