I can tell you how attrition works in Dungeon Fantasy, which doesn't match up with any of these four, but seems to work pretty well so far IME.So @Yora was posting recently about how D&D doesn't work for his style of play. Some of the concerns expressed are flavour-based, which I won't comment on except to say that Yora's experience is different from mine. However there are also some mechanical issues expressed which I think are worth talking about.
I gather the mechanical issue is that D&D tends to be attrition based, requiring the management of resources (primarily spells and hit points) over the course of a day. By default this requires an in-world environment where the opportunity for/risk of combat occurs frequently over the course of a day. ...snip...
If you handwaive that, and check much less frequently, than the assumptions surrounding attrition change since they may only have a fight every few days, which leads to the "all-in resource" fight problem and little meaningful drain on resources at all (since you can stock up on healing magic and blow it on the off days).
Also, random encounters fail to meet their required function because they don't drive behavior (the decisions regarding route and mode of travel having largely been made at the commencement of the journey, and the fights don't serve as a means of applying consequences through attrition). This means you need another method to make the choice of route and mode of transportation meaningful, as you can't rely on established game structures. Here are a few possibilities I thought of:
1. Like Alexis Smolensk, you play out every hex, and it takes years of real-world play to actually get anywhere.
2. You react to choice of route/mode with wanderers as usual, but you use less of them, and make the individual encounters more dangerous (higher risk of TPK, frequent use of save-or-die and save-or-suck, expect to see medusas, basilisks and level draining undead).
3. You have fewer encounters, but each "encounter" is really a mini-adventure, so that the assumptions regarding attrition function inside of the encounter. Because you have time to write adventures to occur between your adventures.
4. You tell the PCs they arrived without significant incident (thereby making choice of route/mode essentially irrelevant, and making your players wonder why a month long journey through the frontier is safer than the area immediately surrounding your average village).
I'm not really happy with any of these. So I am asking whether you have problems like I have described regarding either the game outside of the dungeon, or regarding lengthy overland travel, and if so how you deal with them.
Dungeon Fantasy, being GURPS-derived, is very tactical and a bit swingy. A moderately-unoptimized but forewarned party of five fighting a peshkali (six-armed demon-snake lady, basically a marilith with no magic except supernatural durability like a slasher movie villain) might be able to kill it with good tactics and no casualties 90% of the time, say. The other 10% of the time, something with lasting bad consequences happens, like a front-line fighter losing an arm to one of the peshkali's scimitars, and now your party of five is effectively a party of four with only two front-line fighters until you can get back to civilization and pay the corrupt priests of the sorcerer king to reattach the arm (or ask the poor-but-sincere humble priests of the Father to do the bargain version, which takes a month). The next peshkali or whatever that you meet now has let's say a 35% chance of doing serious damage before you kill it, which could leave you with only one front-liner: attrition comes in the form of the threat of snowballing.
Combine that with a dynamic environment where safe retreat is not guaranteed, either because monsters move around using something akin to an adversary roster (https://thealexandrian.net/wordpress/45091/roleplaying-games/design-notes-adversary-rosters) or just because of the threat of random encounters. Either way, the fact that pressing forward/going deeper commits you to facing a greater number of threats on your way out--no matter how many PCs are still alive and uncrippled at that point--increases the tension.
So the danger isn't so much about running out of HP as running out of combat-effective PCs. A wilderness encounter in which an Undershark burrows underneath one of the PCs and drags them under the sand, but fails to bite off any limbs before one of the PCs stabs it in the roof of the mouth to pierce its tiny brain... The PCs may not be down any HP by tomorrow thanks to healing magic, but they feel more stressed about voyaging nine more days into the Great Wastes than they would have if they hadn't fought the Undershark, because who knows if they'll be as lucky next time. (And maybe the Undershark's bite carries sewer rot, and the bitten PC may be feverish and mildly impaired for the next few days, -1 to all DX-based skills.)
Having consequences that can last for days or months makes encounters dramatically weightier than they are under the D&D 5E model of "everything heals when you rest for 8 hours". I think Yora would find it easier to GM his style of D&D in Dungeon Fantasy than in 5E. You don't have to pad your adventure designs with monster chaff, and even an encounter which the PCs are definitely going to win is still pretty interesting to GM (up until the point where the players are using tactics that are clearly good enough to trivialize the battle, as opposed to just winning the battle--we're discussing this case on the Muster thread right now but the solution in this case is to either stop rolling dice and narrate an end to it, or find some other way to keep the GM entertained--but the point is, it's not like 5E where essentially ALL battles are boring and have no consequences).