I didn't at first, but listening I can kidn of hear it. Since Im a nerd, I had to look and find similarities. I mean the melody is slightly different, but the prechorus' to this and Best of Me are fairly similar and end on the first note of the key (which isnt saying much haha) and have a break and only a semitone difference in key, so i can see it.
When I first listened I got more similarity between the two with the octave guitars in the intro and reintro after the first chorus. Different melodies of course but same concept.