Certainly depends on a state by state basis. No surprise that the Montana folks are saying 400" bulls are more common than 200" deer based on our season structures and management/mismanagement practices. Obviously not everything gets entered, but just look at Boone and Crocket entries and you'll see 10 400+" bulls since 2015 in Montana to only 3 200+" deer in the same time frame.
It's not uncommon to get a couple photos of 400+" elk any given year from Montana, where I can't say the same for deer.
I imagine Colorado would be the yin to Montana's yang and show the exact opposite. Across the west, deer may have the edge on elk with Montana being an outlier due to how poorly we manage our deer versus our elk.
*Edit: Looked at Montana's entries on FWP site and the numbers since 2015 are: 11 Elk officially over 400"; 2 deer over 200". Extended back to 2000, 12 deer, 18 elk. Similar enough numbers to B&C official website.
As for meeting Minimum scoring for B&C- 248 deer all time in Montana, 339 elk.
Again, Colorado would show an entirely different data set, as would Idaho, Wyoming, Utah, Arizona, Nevada etc.