I've listened to Ludwig Schunke's Piano Sonata, Op. 3 before, and my favourite movement is its second movement (a scherzo), so I got the sheet music and tried to play it. It was surprisingly easy and, partially as a result, very fun!
I was perplexed by large swathes of the score implying that I should play them with my hands crossed:
I thankfully get to stop playing with my hands possibly crossed at the start of the last line/system above, but that's 11 straight measures of piano music that might be better played with the right hand playing the lower staff and the left hand playing the upper staff.
The second movement, according to http://ks.petruccimusiclibrary.org/files/imglnks/usimg/3/31/IMSLP187196-PMLP321465-Schuncke_op.03_Klaviersonate.pdf, even sometimes assigns the 16th-note runs to the lower staff instead of the upper staff.
So, am I better off playing this and similar passages with my hands crossed or with my right hand playing the lower staff and my left hand playing the upper staff? My left hand can pull off its 16th-note runs.