At the time, you could get good accuracy out of either clocks or lunar distances. However, it required either really really highly trained trained and disciplined crew (for lunars), or very very expensive clocks. If you're just using lunars, you have to be quick about it to get a good fix, and then you have to do a good job of your dead reckoning to track your position until you get another absolute fix. In any sort of poor conditions, your dead reckoning quality will go down, and your ability to take another absolute fix goes down. That is, you have to dead reckon for longer periods (potentially a few days). Further, over time your dead reckoning estimates will drift by as much as your clock is bad (since you must have some sort of clock to dead reckon even if you get your longitude from the moon).
With an expensive (frightfully so!) clock, you get a better initial absolute fix, depending on how expensive your clock was. However, you can get location fixes more often, with less visible sky, so you don't have to dead reckon for as long as often. You also find dead reckoning easier, since you have a good clock to base your estimates on.
The admiralty found the lunar distance method acceptable because they were already dependent on highly disciplined and trained crews for fighting, and for their existing navigation. The only real problem they ever had with clocks was the expense. Even so, for more important voyages (e.g. James Cook's exploration of the Pacific) and larger flotillas, they paid up. Once the prices dropped, clocks won out.