I5-8400 is directly aimed to R5-1600, intel slashed their margin for that one. It also obliterates 7700K's worth.
So at this point ryzen is not cheaper, yes, except if you go 1700. Plus, if you really wants to get big bang for your buck DDR4-2400 is not going to cut it. Get at least DDR4-3000. Memory and ssd prices is insane these past months and will continue to be so until end of 2018.
I also agree that building a portable desktop like your plan, is, well, why not buy a laptop like normal people?
Then there's this SFF premium - going small have their price... your friend doesn't understand that - just like I can't comprehend paying 400$ to get a seat at any concert.
Where I'm from you can get atx tower case for 25-40$ and 30$ for psu. But it would just be another box I'd have to hide.
Regarding your build, I myself leans towards amd but if you game more than productivity then 8th gen intel is better. You also won't need better ram.
