S&DS 2380 and 2410 overlap substantially but are quite different, and choosing one over the other involves tradeoffs. They both formally require multivariate calculus as the prerequisite (either Math 118 or Math 120, or a previous multivariate calculus course).
If you are planning to take further statistics courses such as 2420 and 3510, then the more standard choice would be 2410, and I’d say you can’t go wrong with this choice. S&DS 2410 has been taught for a very long time, and the courses 2420 and 3510 were designed to follow 2410.
S&DS 2380 was added to our course offerings more recently. Our original question motivating the development of 2380 was: for a student who is thinking of taking just one course in the whole area of probability/statistics/data analysis, hoping to learn as much as possible in one semester, what would we teach them? It has turned out that many S&DS 2380 students go on to take more statistics (including declaring a statistics major), but that was the original concept.
In contemplating taking S&DS 2410, you should definitely not worry about not having taken a statistics course before, and it is not true that 2410 is less suitable for people with no prior experience with statistics than 2380 is, since they both assume no prior experience with statistics, and just assume some basic familiarity with the tools of multivariate calculus.
What are those tradeoffs? S&DS 2410 focuses on probability theory and tends to emphasize mathematical developments more, and S&DS 2380 includes a substantial number of statistics and computing together with some math. That is, typically (of course it varies with different instructors) S&DS 2410 feels more like a math class, and S&DS 2380 mixes in statistical inference (from a Bayesian viewpoint, which is a bit unusual for a course at this level), computing, and some data analysis. You can expect to get more time and practice and depth with Probability Theory in 2410 than in 2380. S&DS 2380 includes topics that overlap (but from a somewhat different point of view and perhaps for different purposes) with 2420 and 3510, such as using likelihood for statistical inference (which also is done in 2420) and Markov chains (which are also done in 3510). From that point of view, students who come out of S&DS 2380 and then take 2420 or 3510 may feel that they are already comfortable with some concepts that others in those classes are seeing for the first time, which could be viewed as an advantage, but they may feel that their command of probability theory is being taxed more than the students coming out of 2410, which is a disadvantage.
In 2380 you would get enough probability theory that you would be prepared to take 2420 and 3510, and in this regard differences between how well individual students “got” the respective classes (2380 or 2410) are probably more important than which class they took, but the median student in 2410 probably has a more solid command of probability theory than the median student in 2380. The 2380 students probably have some additional useful perspectives and insights (as well as skills in computing and simulation) that could help them understand and appreciate some of the things they are about to learn in 2420 and 3510, and the hope would be if they feel a need to strengthen any particular aspect of probability theory while taking 2420 and 3510, it would not be a problem to do some review or a bit of extra reading, perhaps in a 2410 textbook.