There are many YouTubes of both slide guitar and mountain dulcimer - considering how similar their playing techniques are, they've ended up doing very different things.

You can retune a slide guitar to make it sound a bit like a mountain dulcimer. You can't do the opposite, so the slide guitar wins on flexibility. On the other hand the dulcimer has a deep, important and unique tradition in the US. I'm not even in the US, don't play the dulcimer or much American music, but Jean Ritchie did more to inspire me to get into folk music than any other performer.