As seen from the other answers, people have very different experiences when it comes to comparing a round-trip to the two legs being ordered separately.
Historically, things have gone a bit like this:
aA round-trip was just the cost of the two legs
thenThen discounted fares were introduced (so-called APEX fares). The idea was to make sure business travellers (whichwho supposedly have more money to spend) spend more than holidaymakers. This was done by imposing rules on the whole trip, such as the obligation to spend at least one week-endweekend at the destination, or a minimum duration at the destination. To make this possible, it required the round-trip to be sold at once rather than the two legs being sold separately. This is what introduced the big difference between the round-trip (which is discounted) and separate flights (which are not). Note that you usually see only the lowest fare, but rest assured that there is still a full-fare round trip-trip in the system with the same cost as the two legs.
thenThen low-cost carriers came in, and decided that low fares were for every oneeveryone, and that the only important factor for them is whether the flight is in high demand or not. Usually at LCCs, beyond an usually small admin charge / booking charge / credit card charge, a round-trip is exactly the same cost as the two legs put together. And I believe most don't care if you don't use one of the legs on a round-trip.
ofOf course the incumbents had to do something, and you end up with a pretty interesting situation: if there are LCCs with a significant share on that city-pair pair, then they apply fares (and possibly rules) close to those of the LCCs. If not, they continue to apply the usual round-trip-with-conditions-is-cheaper rules.
The end result is that on most popular short-haul/medium-haul routes, there is little difference between the two (at least in term of cost -- the incumbents may still apply sordid rules), while on long-haul routes (where there are few LCCs if any at all), or less popular short-haul/medium-haul routes, you still can see a big difference.
Now, when it comes to picking one over the other, pay attention to the fare rules. Usually when flying with a LCC (at least the major ones), you won't see much of a difference between the two in terms of flexibility. You'll just save a few bucks/quid/euros and a few minutes booking as a round-trip. When flying with an incumbent, all bets are off.