I am a future PA student, and I've worked as a PT Aide in an outpatient clinic for over three years now. I actually applied to both PA and PT programs this year (my third round of applications to PA school, and applied to PT as a backup), and was accepted to both. I can probably shed a bit of light on my experiences working closely with PT's and the application processes.
I have always been passionate about becoming a PA, and that was always my goal, so my first piece of wisdom is to figure out which one you are more passionate about because that will be your career. Shadowing people from both professions will help give you more exposure to figure this out. As others have said, there are different specialties and areas you can work in either profession that expose you to blood and those that do not. I do believe with more exposure you may end up getting used to it though. From my experience, both professions are growing at crazy rates. PT's now graduate with a doctorate degree and direct access is available in most states, which means in most cases patients do not need a script to seek therapy and PT's are trained to diagnose and treat/refer out as appropriate. This does not mean that there is not your fair share of sucking up to physicians (to my dismay, not so much PA's), which in most cases is not how the PT's want to be spending their time. Like I've noticed with PA's, PT's also struggle with some professionals to get the respect that is (usually) deserved, though I'm sure this phenomenon is far more widespread than these two professions. As for PA's, the future jobs and career outlook has skyrocketed in recent years. I was more attracted to the PA Profession because of the variety and freedom of switching specialties, the shorter and more affordable education and training (relative to other healthcare professions, and depending on the program of course), the content and responsibilities of the actual profession, among many other reasons. I became a PT Aide to get hours to apply to PA School, and although I truly respect the PT's I work with and I believe I could be happy working as a PT myself, that was not my passion.
I have actually shadowed a ortho PA that began his professional career as a PT. We talked a bit about why he switched professions and I believe his reasoning behind it was along the lines of he was looking to have a larger impact and more control over the future health of his patients and he was more interested in the medical side of ortho as opposed to rehab.
As far as applications go, in my experience PA school was much more competitive. Take that with a grain of salt, however, because I only applied to PT school this past year after I had years of experience as a PT Aide. After taking this into consideration, I still believe PA school is more competitive and requires more of the applicant. The fact that you're already considering this as a first year means that you stand a great chance at achieving your goal, whatever it may end up being.
Best of luck, and let me know if you have any questions!