I have one of each also. The hourglass I have is a Folkcraft. The teardrop I made myself in a class. To me the teardrop sounds louder and better (could it be that I'm biased, sure). Both slide around in my lap even with the strap on. I think this is because when I play I'm usually on the couch and not sitting straight up so my legs are not far enough apart. But I use that strap to counteract this and can usually control the sliding around enough. Plus I usually tap my foot anyway so it's bouncing up and down too. Overall I would say I prefer the teardrop - again I'm probably biased but that's ok. 
I have 2 hourglass and 1 teardrop. No trouble keeping any of them in place on my lap. I have a slight preference for hourglass due to aesthestics, not sound.
The shallow bodied, slope shouldered, tapered scrollClifford Glen dulcimer in what is known as the 'North Carolina' patternis my absolute favourite dulcimer shape. It does surprise me that none of the larger workshops has ventured into this pattern as, in my book, it beats the Kentucky hourglass hands down for aesthetics
I only have an hourglass but if I buy another dulcimer I would want the teardrop. I would tune them different and be able to remember which is which.
TW
I have one of each. Like them both. Some tunes sound better on the teardrop and some sound better on the hourglass. Since 3 points define a plane (in geometry) I find the teardrop rocks less when you really hard strum. Kind of like the difference between a 3 legged stool and a 4 legged one - the 4 will rock and the 3 will be stable. my 2 cents
I build both hourglass and teardrops. I prefer the hourglass just because I like the look of that shape.
Ken
"The dulcimer sings a sweet song."
I build hourglass dulcimers for sale because that's what most folks like. But my personal playing dulcimers are mostly teardrop. Teardrop's have a distinctly different sound, a more focused bolder sound. That is why you see them more in baritone and bass instruments. The problem with most of the teardrop's on the market are made too skinny and unsubstantial. I found that building them with a wider bout they sit quite well on my lap. I also like the elliptical shaped Galex design. I built a very wide body model that plays best on a table top. Never played a box dulcimer, something to look forward to... All dulcimers are fun to play no matter what shape your dulcimer's in... Bob
I meant the Simerman shiftsto my RIGHT - dyslexia!! 
Linda W. Collins said:
Hi James,
Working with a variety of students, with a variety of body shapes, I find the hourglass to be preferable from an ergonomics standpoint. The teardrop can be difficult for some folks to get positioned in a stable fashion against their belly! The only difficulty I've had with an hourglass shaped dulcimer is with the concert model Simerman; it tends to shift around my body to the left, due to the large lower bout, so that I have to periodically "retrieve" it!
Linda
Hourglass for me too Linda. I'll always be one of "your beginners", and you are absolutely right. I've purchased several tear drop dulcimers and ended up selling them all on this forum or ebay. Now, if I could just get rid of my little pot belly.......I could...........hmm.
I have not played a tear drop shaped mountain dulcimer, but have wondered about them so it is a good question.
I have two different sized hour glass shaped dulcimers and I really like playing my shorter one, my longer one slips a little bit, but thus far neither have slipped off my lap.
Interesting observation Linda, nice to know.
Hi James,
Working with a variety of students, with a variety of body shapes, I find the hourglass to be preferable from an ergonomics standpoint. The teardrop can be difficult for some folks to get positioned in a stable fashion against their belly! The only difficulty I've had with an hourglass shaped dulcimer is with the concert model Simerman; it tends to shift around my body to the left, due to the large lower bout, so that I have to periodically "retrieve" it!
Linda
