I've been using Dunlop Tortex triangles (or as I like to call them... pizza slices) for almost 20 years. I use the yellow ones for acoustic and electric guitar because they have a bit of flex but are still stiff enough to really dig in (perfect for shredding out metal/punk riffs) but sometimes I'll use the green ones which are a tad stiffer which makes really fast single note soloing a bit easier/more accurate (but the yellow ones are better for general soloing I find because I like to "rake" and screw around with picking dynamics). I use the green or purple ones for bass (green for a softer and more dynamic attack/purple for faster/precise/harder/even dynamics).
I use the ones with the slightly more rounded tips... not the ones with the ultra sharp points. That allows the pick to slide off the string more smoothly (the sharper ones tend to slow down playing, break strings and are just awkward all around... they're okay for bass though I guess).
I switched to Tortex IMMEDIATELY after I first discovered them for a whole pile of reasons.
1) They don't "explode" on me. Seriously. Those plasticky "Fender" type picks crumble between my fingers in no time. Just shatter into a bunch of pieces because I guess I play so fast/hard on the wound strings and dig into the sharper unwound strings so much. I'll be playing then realize I lots all my attack and/or feel something weird going on and sure enough the tip of the pick will be gone and the rest of the pick split in two. Terrible. The Ernie Ball "plasticky" ones hold up a LITTLE better (I used to use the pink ones which seemed to have a better chemical composition than the Fender ones) but eventually the same thing happens. Off brand picks? Fuggedaboutit. Toast almost immediately.
2) They wear down much more smoothly/evenly. All the other picks (when they survive) get burrs that catch the strings or they widdle down in bizarre ways that make them annoying to use very quickly. They also stand up to pick scrapes a lot better. I can get one pick scrape out a Fender pick and it's toast. Nylon picks deal with scrapes a little better but the grooves (and burrs) caused by scraping snag the strings a lot more. Like the burrs are more "tacky" and I start breaking strings/can't get proper pick dynamics going. Nylon picks generally become useless to me very quickly due to that burring and tackiness even without pick scrapes. They just get all rough and grabby on the strings instead of sliding off them smoothly like the Tortex ones or a fresh Fender/Ernie Ball pick.
3) Tortex doesn't get all slippery when your fingers sweat. They don't have the same grip as the nylon picks with little bumps but pretty close to it without the bumps (which feel weird to me anyway... get's in the way of my pick dynamics). The Fender/plasticky ones have zero grip when wet and harder any even when dry they get all slippy. This causes a situation where you have to grip them harder (which screws up picking dynamics) or play softer (suxxorama).
So that's just the Tortex material itself. For the pizza slice shape I think they are superior because...
1) More much more grip area. I have "big" hands (they are skinny but long... just like me... please no wiener jokes, lulz) so regular sized pics are very fiddly to me. The extra length and grip allows me to choke up and back off the pick much more (thus providing much more dynamics). I can get a really good strum going without that extra space and if I need to get into pinch harmonic territory I just choke up. That choke up/ease back handling of the pick also becomes way easier do to the extra handling room and I'm much less likely to drop the pick because of it.
2) Instead of one tip I've got three. So essentially I'm getting three times the useable pick life out of the pizza slice style because as one tip wears down I can just use one of the other two tips. Also it means I don't have to worry about which direction the pick is facing like I would with a standard pick. We've all had that moment where we've realized we're using the blunt end of a pick and had to reposition it on the fly... I freaking hate that. It also makes it so when you drop a pick live you don't lose that microsecond of time/brain power making sure you have the pick pointing in the right direction.
3) Due to the angles (which are wider than a regular shaped pick) it contacts the strings in a way that is a little smoother/more desirable to me. It's not as staccatto as a sharper angle pick so strums and trem picking stuff isn't as ridgid. You control that instead by decreasing the angle of the flat dimension of the pick in relation to the string. So it does have a style altering effect that takes some getting used to. It also does sometimes cause undesirable scenarios which is why I have, partially, started sometimes using regular shaped Tortex picks to record certain things with... which I'll blather about before wandering off again.
I have been having a much harder time getting a hold of my beloved Tortex pizza slices. I haven't set foot in a music store in years due to my disablities and poverty. I've been relying on internet stores (and ordering online from music stores) when I get a chance to actually buy stuff and always try to get stocked up on picks when I do. They seem to ALWAYS screw up my pick orders though. I used to just snag them whenever I was picking up strings in person if I saw they were in stock. Now it's up to the counter staff at these places to know WTF I'm talking about and they ALWAYS screw it up. I have tons of the normal shaped Tortex picks now due to these screw ups and limited supply of the pizza slices. The last time I made an order and they actually had the pizza slices in stock I told them to send me a mountain of yellow ones and a bunch of the green and purple ones. Instead I got THREE yellow ones then a bunch of all the other colors of the rainbow... most of which are WAY too thin to use (I cannot play with those sh*tty paper thin picks... at that point you might as well just use your damned thumb because that's pretty much what you're doing anyway).
So I started playing with the normal sized ones again and for some types of soloing they are actually better/more precise. Since I don't play live anymore a lot of my needs for the triangles aren't a factor (I'm not sweating and if I drop a pick it's no big deal). Still it really is only some specific tasks where they are better and a lot of the time if I switch over to the triangles the parts flow and record WAY better.
I'm just trying not to wear down the slices I do currently have into nubs before I can stock up again which will hopefull be soon. And this time I probably will drag my sorry gimp ass down to the local music store who just got taken over by one of the big Canadian chains and, if they stay true to their franchise, with have them in stock or order them for me.
Now how's THAT for being a persnickety spazz about picks? lol... It, to me, is a massively important issue for guitar players though that doesn't get nearly the attention it deserves.
PS: Before Tortex I used to use Big Stubbies (yes the big ass cough drop looking ones) because they were the only ones that allowed me to dig in without shattering. They are pretty ridiculous though and I can't even believe I recorded an entire studio album with those buggers.