I visited this before the Babylon Exhibition. I actually saw the crypt first, as the entrance via that was the first one I came across.
The crypt is packed with burials and memorial stones: mostly they are individuals I've never heard of but some to famous people and some to this group of war dead or that. The Nelson and Wellington tombs are huge; there's space yet for a few more of comparable size, but it would take that many more to get seriously crowded. Upstairs Wellington gets another huge memorial.
I got up into the Whispering Gallery (~260 steps up), but since I was on my own lacked anyone to whisper to. Nice views of the interior of the cathedral though. The Stone Gallery (another ~120 steps up) is a good vantage point for looking out over London though the rather narrow gaps in the stone don't make it very convenient. Unfortunately the Golden Gallery was shut so I didn't get to see that. As you can imagine after all those steps I was quite tired.