Okay, we've got a genuine disagreement then. You think average mixed party will improve as much against Banshees by going from 5th to 8th as the Banshees do from getting more Banshees (twice as much XP, whatever that works out to be). I on the other hand look at the factors you list (initiative increase, possible spell DC boost from ASI, possible saving throw boost from ASI) and see them as negligible factors (+10%-25% maybe) compared to the 100% increase in Banshee. Since we're both interested in this question, do you want to collaborate on a scenario to test this?
*snip*
CR is so bad in 5E that you're IMO better off mostly ignoring it and just focusing on environmental factors and raw monster abilities. The encounter tables will give you a precise number N of Banshees whom the 5 8th level PCs can face in the crypts and still defeat. (N=4, 4 Banshees is a Hard fight for them.) The encounter tables will also tell you that N+1 Banshees is Deadly in the Crypts, but Hard in the sunlight above the crypts (reduce difficulty by 1 step for favorable environment). My judgment tells me that one of both of these ratings is wrong. The one in sunlight is definitely wrong (it's more like fighting 10 zombies than 5 Banshees, and even 22 zombies would steal be an Easy fight even by encounter building rules). The one in the crypts is probably wrong, possible TPK, but it's difficult to evaluate in isolation except to say that even (or [/COLOR]especially!) a tactically-smart party would far rather face 9 Ogres in the crypts below the city (10,125 XP) than 4 Banshees (8,800 XP). The Banshees are worse. If that's non-obvious to anyone I would gladly run the encounter for you.
So I ran a couple of encounters with a "standard" 4 character party. I used the 5th level melee fighter, life cleric, evocation wizard, and rogue. The 5th level party had 2 banshees for a hard encounter. For the 8th level party, I bumped the primary stat to maximum. The fighter's extra ASI was split between Con and Wis which bumped both those stats. The 8th level party had hard encounters vs. 3 banshees. I ran 3 encounters, 1 at 5th and 2 at 8th. I did not really have time to do more. I used the same initiative, which was rolled at the beginning, for every encounter. The initiative was B1 C W B2 R F (B3). The one thing I added to the initial level 1 equipment was a potion of healing to pop people up when they went to 0 hp. The encounters started assumed everyone could reach someone to attack on the first turn.
The encounter at fifth was a long, drawn out affair. The initial wail took out everyone except the Wizard (!?). The wizard made note of where the cleric was, cast
fog cloud, and sneaked over to the cleric. The second banshee came to the edge of the fog cloud and let out a wail. The wizard saved again. The first banshee was failed an Intelligence (Investigation) check to find the wizard in the cloud. The wizard gave a potion to the cleric, and a couple more failed Intelligence (Investigation) checks later, the cleric used preserve life to get everyone back on their feet. The wizard dropped the fog cloud and gave the fighter
magic weapon (although it should have been give to the rogue in retrospect). Several rounds later, the banshees were dead, and the party was able to rest and heal from low hp. This encounter may have been a TPK if the third Banshee was in play.
The first encounter at 8th level was a slaughter. The first two banshees wiped everyone out with their wails in the first round, but the banshees were unable to hit anyone for a couple rounds even with advantage. The wizard eventually rolled a 20 on a death saving throw, noted where the rogue was, cast
fog cloud, and crept over to the rogue. The banshees failed intelligence investigation checks to find them. The cleric and fighter had bled out. The rogue rolled a 20 on a death saving throw as the wizard got there, and the wizard used
dimension door to get them out of the area. The third banshee was absolutely useless. If this had been a 5th level party, it would have been a TPK at 5th level, but the 4th level spell saved two of the party.
The second 8th level encounter was a cakewalk. The cleric survived the initial wail and cast
silence over the party. The party hunkered down, protected the cleric, turned some of the banshees, and fought them one at a time.
A few things I noticed not all of which are a difference between the 5th and 8th level party:
* Like most special abilities or surprise, this is highly dependent on initiative as to whether the party has a good chance at survival.
* The extra ASI helped with damage, saving throws, and spell DCs.
* The cleric is a pivotal piece in this encounter. Preserve Life, Turn Undead, and
silence are all game changers in this sort of encounter. At 6th level, the cleric gets the second channel divinity which helps make sure that no one dies. Preserve Life can pull the whole group off the floor, and Turn Undead can make it so the party can focus on one banshee at a time.
* Horrifying Visage is not that big of a deal. An affected creature does not have to run away and still has a reasonable chance to hit even with disadvantage.
* The 4th level spells can save (some of) the party or at least make a big difference.
* The extra damage made a difference in the last encounter to overcoming the damage resistance of the banshees.
*
magic weapon can make a big difference against the creatures that have weapon resistance if magic weapons are not in the party. The 8th level monk and moon druid would essentially be doing double damage compared to their 5th level versions.
Shillelagh would also be very useful.
* Anyone who survives the wails is probably going to survive the whole encounter.
The first encounter encounter might have gone worse for the 8th level party. The first 8th level party encounter definitely went better than it would have for the 5th level party, and the last encounter was probably easier for the 8th level party because of more resource, but it might have been about the same. So from my limited look at 3 encounters, I would say that the 8th level party will do about as well as the 5th level party while fighting twice as much encounter xp of banshee as the 5th level party.