It sounds to me like the issue may be that you're crowding the pan.
Basically, to get everything nice and brown and crispy, you need enough space for all of the steam to escape. That picture you showed has potatoes stacked on top of each other -- that means as the bottom items cook, they're going to end up steaming the items above them.
At a diner, they have a large griddle to work with -- they can really spread things out. You're not typically that lucky in a regular kitchen, as you don't have as much space, and you have a lip on the pans that'll hold the steam in.
So, either work in smaller batches, or consider recipes that use an oven -- using sheet pans instead of a pan on the stove solves much of the problem.
One other trick is that most diners don't start from raw potatoes -- maybe with hash browns, but not for home fries, you're not going to get the nice soft interior in a reasonable amount of time unless you start with a potato that's already been baked or boiled. (If you're doing things in the oven, you might be able to, but not in a pan)
Just for reference ... I have a 14" cast iron skillet that I use for home fries ... and it's about the right size for cooking a single large potato, which might be two servings, maybe three for kids. (I tend to cook carb-heavy meals).
update : I probably should've stated this directly -- you want the chunks of potato to form a single layer in the pan, with space in between them.
I used to cook plenty of purple sweet potatoes when I was living in africa:) Sounds like you maybe cooked them too long...
They can be extremely tasty, sweet with a "perfumy" hint if you are lucky. They are best boiled with the skin on like you did and peeled afterwards (as the taste is preserved better that way). As for cooking time it really depends on the size (which means the potatoes are likely done at different times) but you can always feel when they are done by pressing on the potato with a fork - it should give slightly/be soft. I think it usually took me about 30min but I didn't use a clock. It may shorten the cooking time slightly to make holes in the potatoes with a fork (this also adds to the "creaminess").
I guess they do sometimes get a softer, more "creamy" consistency than your usual potato when well done. However the taste is richer and in my opinion far superior to orange sweet potato. If you prefer a firmer potato, just let your potatoes stay on the firm side (in my experience, though, the taste is enhanced by letting them go soft). But boiled ones would anyways mainly be for puddings as it gets rather sweet.
For panfrying I would suggest avoiding boiling the sweet pots first. Simply peel/wedge them raw, fry them as chips until done and serve with a spicy/hot dip - yum.
Best Answer
This won't apply to all stews, but if there's something acidic in the liquid (such as tomatoes or vinegar), some items will not soften or break down as quickly.
I know this includes both potatoes, onions, pasta and rice, but I would assume that other starchy vegetables would have similar behavior.
But there can be other factors in play, too. Many people cook potatoes to mash in a fair quantity of boiling liquid, while many stews are simmered. As stews often have liquids other than water, we avoid taking them to a full boil for a few reasons: