Op it depends on context. Night work is harder than day work (Acc to Dh) as even if you sleep during the day, you don't get the same sort of sleep as you would at night due to all the daytime noise, even if it's on a subconscious level. Then you've got to stay awake when you would normally sleep and work.
The day before nights Dh generally has a long lie in and then a nap again mid afternoon to ready him for working the night.
During his nights, Dh generally helps me get the dc breakfasted and dressed, then goes to bed when he gets in from nights and rises between 1-2 hours before he needs to be at work, depending on what's happening at home. On the late afternoon where I do volunteer work, he is up just before I leave and the agreement is he goes to bed as soon as he gets in the following morning, to make up for the disruption to his sleep.
And as easy as it would be to say 'don't compete over who is more tired' when you are in the throws of sleepless nights and poorly baby days, you just don't think straight. I have been there and been as unreasonable. However, Dh ensures I get my lie in time when he's back off nights to make up for the loss of sleep I have had - I do not cope well on disturbed sleep. Does your Dh do this for you? When he has had his long lie in, does he take over with baby care until he goes back to bed for his nap?
When you are back at work, you might find it easier when Dh is on nights as you won't be home when he's sleeping, so he will get a better rest.
As for the housework, quite frankly the week Dh is on nights i do the bare minimum and Hoover when he has gone as I'm doing sole care for our dc. Don't try to do everything as it's a swift route to resentment and arguments.