I possess both and alas, I do not play them nearly enough. Partly that's because I'm just not comfortable hunching (well, siting) over an instrument -- I like to sit back clutching a little lute, like an 'uke or mando or small guitar. I play my smaller mountain dulcimer occasionally because I *can* hold is close and chord it.
CV: mountain dulcimer was my first stringed instrument over a half-century ago. I built and sold MDs for a while. I plan to build more -- but not for playing with a noter and plume in my lap. I am totally sold on strumstick-style playing.
My lap steel is a late-1940s heavy sandcast aluminum Aloha with case and amp, made in Hawai'i, that I bought decades ago for about US$25. If I read the listings right it could now be worth up to US$1000. I may sell it sometime soon because I just have not played it since forever.
That said, some folks love these instruments, love the playing positions, love the way they interact to make music. Dulcimer and HSG (Hawai'ian steel guitar) sites exist.
Taropatch.Net covers HSGs as well as Taropatch 'ukes and other Hawai'ian music.
EverythingDulcimer.Com covers MDs as well as bowed and hammered dulcimers.
FotMD.Com (Friends of the Mountain Dulcimer) specializes in, guess what?
Both MD and HSG / lap steel guitar differ greatly from 'ukes, mandos, guitars, banjos, etc both in playing position and tunings. Lap steel means holding a slide and tuning open. Dulcimer can be played on lap or held, in drone modal tunings (many of them!) or chordable tunings. You *can* have lots of fun with both, and they'll point you toward different approaches to music.