Brother John, Carol and searcher have zeroed in on what I think are the key points; I just want to elaborate on a few issues that bear on what they've told you. The bare bones of the story are that
(i) weight-trained muscles are not only bigger but faster, because, as numerous, well-designed studies confirming the increased speed of movement generated by larger muscles suggest, part of normal hypertrophy is progressively greater synchronization of muscle activation by the neuromotor groups involved. In fact, the very first phase of weight-training a muscle group leads to strength increases that are not due to muscle size but to this firing-in-synch of the neural units that drive muscle fibres that are already there `in place'. More synchonization translates to faster response times; and...
(ii) ...the problem with bodybuilders is not that they have powerful, well-developed muscles; it's how they got those muscles—now, almost universally, anabolic steroids. Same with many other athletes (remember, it was powerlifters who were the first American guinea pigs for John Ziegler's disgusting abuse of his medical credentials by making anabolic steroid available to those athletes; but the East Germans, Bulgarians and other Communist bloc athletes, swimmers and runners, had been using them for probably a decade or more in Olympic competition, and those were the ones who let Ziegler in on the secret). The problem with steroid-and growth hormone-inducedmuscle growth is that muscle tissue development can be, and routinely is, forced beyond the natural limits imposed by skeletal structure. Connective tissue cannot keep pace with the excessive development of muscle size through abuse of anabolic substances, and serious injuries will inevitably result (Dorian Yates' forced retirement as a result of repeated muscle/tendon tears off his arm bones is a glaring high-profile example, but the history of contemporary body building is litted with stories like his).
So if you're training strictly naturally, then no matter how big your muscles get—and there are limits imposes by your skeletal structure to natural muscle growth, make no mistake!—you can only get faster as your muscles grow larger. Explosive strength, which is what muscle growth promotes, and increased neuromotor syncrhonization, are going to translate into faster reaction times, all other things being equal. The steroidal monsters that modern body-building chemistry projects turn out have enormous muscles but, crucially, lack correspondingly stronger tendons and connective tissue—those don't respond to externally introduced anabolic stimuli. So you have these guys with maybe a hundred pounds or so of muscle tissue more than the best they could achieve if they were training naturally (I'm talking about the new breed of 300 lb+ mutants who show up with 5% bodyfat at contests), but only have the connective tissue to lug around 200 or less of those pounds...
sure they're going to be `musclebound'. But that's because they are carrying muscle around that they haven't actually earned, but have in effect stolen by using the complex chemical cocktails that they take, and therefore
their muscles are just too big for their much weaker connective tissue to move quickly and efficiently. These guys run cycles more complex than the epicycles in Ptolmey's model of the solar system, juggling four or more major steroids, industrial strength diuretics, growth hormones, plus other drugs to counteract the side effects of these. Pro bodybuilders shouldn't even enter the discussion, for the most part. If you just use a good, high-intensity weight training program of the Sisco/Little or Mentzer type, you'll develop good muscularity in a relatively short time and both your strength
and speed—hence, power—will increase, completely safely.