Hi, i say stick to the physiotherapy degree. I studied the 4 year Bachelor of Physio degree in Australia and feel it gives you good grounding & understanding. However experience is still everything!!!!. I also know my university offered the grad entry physio to exercise sports science students which is only 2 years so really skips alot of stuff. I know when we had prac's during university, we would sometimes be on prac with those students, and they really struggled because they had to somehow learn what we learn in 4 years & do the 36wks of full-time prac experience all in only 2yrs.
Although on the flip side im sure employers who don't know about physio would look at it & be more impressed, however i know in Australia alot of the physio's have the other opinion & perfer to hire the 4yr undergrad physios. However different countries have different opinions.
Since its 3yrs of undergrad sports science & 2 yrs of grad entry masters. Or 4yrs of undergrad physio & 1-2yrs of postgrad Masters Sport Physio, aka same time. i strongly suggest the 2nd that way u have a undergrad & masters in physio & become a specialist sport physio, much better approach. Just so you know, in Australia you are not allowed to go to the Olympics as a physio without a Masters of Sports Physio ontop of your undergrad physio degree. So the sports science & grad entry physio still will not help in that instance.
I think at the moment the best approach is work in the sports feild while at uni, be a sports trainer, a coach, strength & conditioning ect.. these courses are all usually only 1-2wkend . These will allow you to get a good understanding of sports & also possibly make connections for when you finish. I did this approach myself while at university for the full 4 years working as a coach, then strength & conditioning & sports trainer. I then went straight into sports physio when i graduated without working in a hospital or private practice first, because i had made the connections prior to finishing uni.
I wish you the best of luck.