There needs to be a distinction between a top "Shutdown Forward" and an elite "Defensive Forward." It is a lot different, imo.
To me, a shutdown forward is someone who shadows a star offensive player and covers him like a glove. He is aggressively making life difficult for that offensive player by following him, containing him and basically "shutting him down." These guys constrain through any means necessary. Some use speed, some use physical checking but they all play a gritty and tenacious game. For example, Jere Lehtinen is one of the best defensive forwards ever, but he is not a great shut-down forward. One of the best shutdown fowards I've seen is a guy like Bobby Holik. Holik is a great strong centerman who had the reach to shadow and neutralize top players (some who are also 6'4'') like Mario Lemieux and Mats Sundin. He was tenacious but also had the cerebral game to anticipate the moves of some phenomental offensive talents.
An outstanding defensive forward like Jere Lehtinen may not need to be as physical and tenacious to play an overall extraordinary defensive game. They can use their speed and mental game to make broader impact, as opposed to shadowing one player. These guys could cut off passing lanes, position a left-wing lock strategy, aggressively forecheck, skate back to break up developing offensive plays, play a last man back, create turnovers / takeaways by reading plays, etc...
The effects of a great shutdown forward is immeasurable. It can literally break a team's morale when one team's 3rd line center can effectively neutralize another team's superstar. For example, Shayne Corson on Alexei Yashin or Bobby Holik on Lemieux & Sundin.