I don't have a dirt floor and at times I have wished that I did. But after thinking about it, I have some pros and cons in my mind and right now, I'm glad I don't have dirt in the chicken house. I may change my mind on that.
There are lots of pros to the deep litter on real dirt but I won't go into those.
So I'm going to play "Devil's Advocate" for not having a dirt floor.
Here are some things I've thought of for not having a dirt floor:
With wood floor: I put a sheet vinyl on my wood floor to protect it. Then I put in some dirt on top of the vinyl that I dig from under the deep litter in the run or garden, then wood shavings go on top of that.
1. With sheet vinyl -It protects the wood floor; no rotting.
2. It does well and is easy to shovel the indoor litter right out onto the run.
3. Possibly easier to more thoroughly disinfect if there is an outbreak of a lingering disease.
4. I always leave some of the litter to restart the next batch. Though there isn't a fully functioning deep litter indoors, it is "started" from the dirt and some of the prior accumulation and I get a great DL outside in the run.
5. My birds still get the advantage of the deep litter in the outdoor run and the beginnings indoors.
With cement floor:
No vinyl needed to avoid rot. Can hose out the floor if a deep cleaning is needed. No fear of digging predators.
Disadvantages I see to the dirt floor (remember there are a lot of advantages!)
1. Motivated predators can more easily dig under it and get into the coop... including an easier entrance for rats and mice. (Can be deterred by putting down hardware cloth but determined predators can get through if they work at it by chewing, etc.)
ETA: There is also the issue of the frame of the building rotting at floor level if it's on the dirt. Of course, you could put a block or cement area around the perimeter for the base of the shed to sit on.
My current shed floor is rotting from underneath. We put a new layer of osb down when we renovated it but it's feeling soft in spots already.
My worry if I turn it to dirt is the DL will always be wet and soggy.
Don't ask me what dum dum built the barn and shed at the lowest point in the property!