A lot of this decision should rest on what speakers you are using. Speaker specs will tell you how strong an amp you need to power them properly.
The difference in amps can quite often be found in it's ratings. First, the receiver may or may not be rated to drive a 4 ohm load. It may not be able to deliver the current required. Separate amps are generally rated down to 4 ohms and often down to 2 or 1 ohm. Other factors to consider are the distortion ratings. Some receivers will measure distortion at 1% in order to advertise a higher watt rating. Separate amps generally will measure to about .04% or lower distortion. Also, make sure that the receiver's distortion was measured at a full spectrum, 20-20k Hz instead of simply at 1k Hz.
Manufacturers can play fast and loose with testing procedures to increase the advertised watts rating. The trick is to understand the ratings and what they are telling you about the amp. Generally, if you have speakers that are 8 ohm and reasonable sensitivity, a receiver will be fine. But if you are driving 4 ohm speakers with lower sensitivity, a separate amp may make sense.