There is no much difference between that options (except making file as a strict option reduces flexibility of your program).
To compare both approaches, let's check, what stays behind a magical entity FILE*
:

So in both cases we have a FILE*
object, a file descriptor fd - a gateway to an OS kernel and in-kernel infrastructure that provides access to files or user terminals, which should (unless libc has some special initializer for stdout or kernel specially handles files with fd = 1).
How does bash redirection work in compare with fopen()
?
When bash redirects file:
fork() // new process is created
fd = open("file", ...) // open new file
close(1) // get rid of fd=1 pointing to /dev/pts device
dup2(fd, 1) // make fd=1 point to opened file
close(fd) // get rid of redundant fd
execve("a") // now "a" will have file as its stdout
// in a
stdout = fdopen(1, ...)
When you open file on your own:
fork() // new process is created
execve("a") // now "a" will have file as its stdout
stdout = fdopen(1, ...)
my_file = fopen("file", ...)
fd = open("file", ...)
my_file = fdopen(fd, ...)
So as you can see, the main bash difference is twiddling with file descriptors.