Ask HN: Does Google consider .../somepage/ different from .../somepage?

We have recently migrated our system from PHP to RoR.

However, in our PHP implementation, all URLs were of the form: http://somedns.com/hello-there/ and redirects the pages with a 301 without a / to the /.

(e.g. http://somedns.com/hello-there -> http://somedns.com/hello-there/)

Whereas, our new RoR implementation is of the form: http://somedns.com/hello-there and redirects the pages with a 301 that end in / to the no /.

(e.g. http://somedns.com/hello-there/ -> http://somedns.com/hello-there)

Will Google understand that both pages are still the exact same, and leave our SERPs in a good place, or will we lose our SERPs due to the change in trailing /?

If Matt Cutts, a Google Search Developer, or an expert SEO/SERP HN'er could chime in that would be incredibly greatly appreciated.

Our team members are split 50/50 on whether or not this would affect SERPs or not, so it would be great if we could hear some opinions, thoughts, comment, complaints, criticisms regarding all of the above.

Thanks in advance