Hi Jan,
Let me start with saying you should visit both parks!
Yes, Khao Yai receives more visitors, though certainly weekdays (and even weekends) in March are not bad. Kaeng Krachan also is getting more busy; visitor numbers might be quite a bit lower than Khao Yai, but because there are less places to go, it can still feel crowded especially in weekends. In Khao Yai there are a bit more sites spread through the park, so the visitors spread out more; but fact is that at first sight Khao Yai looks way too developed. But walk ten metres into the forest and you will feel like you are in the wild.
I like Kaeng Krachan more, because it feels wilder, but honestly I think Khao Yai is easier to see wildlife, and also to photograph. More visitors means wildlife gets habituated to people and therefore will pose better for photography; same you can see in major African parks, and other popular parks in the world.
As an example, apart from maybe 2 gibbon families around the river crossings in Kaeng Krachan, most other families are very shy and hard to photograph.
Gibbons are never an easy subject for photography, but in Khao Yai chances to find a gibbon family that doesn't 'run' upon seeing you, are quite a bit higher. Then all you need is 'fight' with the light and obstructing foliage. But chances are certainly better than in Kaeng Krachan.
Kaeng krachan also offers less possible activities for visitors. Khao Yai has a larger trail network (and also easier trails; which is nice because you can actually look around for wildlife instead of having to focus too much on where to put your feet or just simply be out of energy to even enjoy the surroundings; some trails in Kaeng Krachan are tough... ). Even in Khao Yai on the trails you usually do not see a many people.
I guess others might have a different view on this, but at least I would certainly not say that Kaeng Krachan is easier to see wildlife; though Dusky Langurs are hard to miss, haha. Both parks are quite different and offer different opportunities for various species, so whenever you can, I would visit both ;-)
On paper Kaeng Krachan has more species, but on the average trips I have done in both parks the list of species seen is certainly not longer than in Khao Yai; more likely shorter. (I am talking mostly about mammals).
About time of year, if you are after mammals, honestly I don't notice too much difference throughout the year. Dry conditions are by many considered good for wildlife watching, and perhaps it is if you like hide photography near waterholes. I personally prefer actively searching for wildlife, and have the feeling I see just as much mammals in mid-wet season as in mid-dry season. For birds I think March should be OK, e.g. hornbills are nesting. For reptiles March is not too bad either, though I prefer it to be more wet.
In the end, I don't think you can make a wrong choice, though you might also notice that finding wildlife is not easy! That's exactly why Thailand is one of the most exciting wildlife destinations. Easy is never fun!
One additional note, if you are after wild elephants, add Kui Buri national park to your schedule.
You might be lucky in Khao Yai, and it requires more luck to see some in Kaeng Krachan (apart maybe from Pala-U area), but I have not heard of anyone being unlucky when visiting Kui Buri.
Enjoy!