Dedicated stream ciphers typically are, or at least can be, somewhat faster than constructions based on block ciphers. (If they weren't, there would be no point in using them, since a block cipher can do everything a dedicated stream cipher can.) What you gain in speed (and possibly code size), however, you lose in versatility:
A block cipher (in CTR / OFB mode) can be used to build a stream cipher. There is no simple way to construct a block cipher out of a stream cipher.
Block ciphers can also be used to construct many other useful cryptographic tools, such as MACs and hash functions. Stream ciphers are typically only good for encrypting streams of data.
In particular, a single block cipher can be used to construct a fully IND-CCA2 secure authenticated encryption scheme. Stream ciphers do not generally include authentication, and thus cannot protect data from tampering.
Several block cipher modes of operation (most notably CTR mode, but also CBC and CFB to a limited extent) have the useful properties of parallelizability and seekability — that is, the en/decryption of different parts of the data can be done in parallel, and it's possible to start decryption from any point in the data stream.
Because of their versatility, block ciphers like AES are also popular candidates for fast hardware implementation. If you have a fast block cipher implemented in hardware, there's a good chance that it'll be faster than any dedicated stream cipher you could implement in software.
All that said, some of the fastest dedicated stream ciphers can be very fast, both in hardware and in software, and many are also designed to be very compact in terms of code/circuit size. If you really only need stream encryption (or random number generation), a dedicated stream cipher may be more efficient than a block cipher.
See also: Difference between stream cipher and block cipher