We know that it's possible to create a hash using a stream cipher (for instance, RC4 or AES in Counter Mode). As stated here: "A Pseudo Random Generator (PRG) and a hash function are both Pseudo Random Functions (PRFs), but they have different security considerations". Whether or not it's advisable to do so, is there a correlation between the way of a hash function being created and its speed? For instance, are cryptographically secure hash functions (such as SHA-1) faster than a hash function created using a stream cipher, or the opposite? Is each case entirely different?
Take this paper as an example. In page 6 you'll see the protocol. As described, the protocol uses a PRG which takes as an input something of size k and produces something of size m. The authors say that they implemented the PRG using AES in Counter Mode. The reason for not using a hash function is because we want the output to vary and sometimes being really big (say 100.000) where when using a hash function the output is fixed (i.e. 160 for SHA-1). For the sake of argument, let's say that the size of the output is not a problem (we use something small like 160) and that we don't take security into consideration.
Which PRG would be faster? A stream cipher (like AES in Counter Mode) or a Hash Function like SHA-1?