I have a few thoughts that hopefully will assist you:
First, the fine print... I don't have any experience converting LAS to DEM, but I do have a fair amount of elevation change detection with LAS-derived DEMs.
Specific to the striping that you mentioned... as a US President once said, "I feel your pain!". In my experience striping (sometimes seen in DEM-derived hillshades, even resembling a hounds-tooth fabric pattern) has ALWAYS been due to improper resampling somewhere along the data handling chronology. With elevation data, NEVER use the Nearest Neighbor option (which is, unfortunately, often displayed as the default option - and thereby easily bypassed). I have found that the Bilinear Interpolation option generates great output without any striping. So I would recommend that you repeat every command and tool used in your process to get the LAS data to its current state and wherever there's a resampling technique option in the tool dialog (for example, it's right there in the Project Raster tool dialog) use Bilinear. For those tools that don't display a resampling technique, click the Environments... button at the bottom and replace any Nearest Neighbor options with Bilinear in the Raster Storage section. It only takes one Nearest Neighbor somewhere in your chronology for stripes to make their unwelcome appearance!
You mention that you have data sets from two different LIDAR projects. You'll need to assure that the two resulting DEMs are a) in the same CRS, both horizontally and vertically and b) exactly aligned to each other in the X-Y dimensions. The latter commonly involves adjusting the DEMs to fit several ground control points (think road intersections) located across the study area. There's lots of how-to articles on the internet if you are unfamiliar. I would also recommend becoming familiar (query GIS Stackexchange) with the snap raster concept found in Environment Settings > Processing Extent.
Even after taking pains to assure that both DEMs are aligned, I've still had to solve weird patterns following subtraction. Happy processing!