I have only played Warhammer 8th Edition thus far, but I will be trying 6th edition soon. To my understanding 8th edition differs from previous editions with its focus on large center piece models, very big blocks for units, and devestating spells. No doubt the changes in 8th came from a need to sell more miniatures, and the rules had to reflect that. The edition started with a focus on big blocks of infantry, and once everyone had bought their fill of infantry an era of introducing monsterous cavalry followed. Once everyone had adjusted to the new meta and bought the new and shiny tools the next big thing became the center pieces of the army which then introduced an era of having that really powerful and mobile toy to dominate the game and its flow.
Warhammer 8th edition is not balanced, so some armies are just better and stronger than others when it comes to pure power, point costs, and the variety of tools available to them in their army book. Some armies also rely more on synergies, and are less forgiving to play, which makes them more dependent on getting as much bang for their buck as possible which more often than not means that they want to play with bigger armies.
The tournament standard for most tournaments I have been to were 2400-2500pts, and most people I play against prefer playing 2500-3000pt armies. Playing a bigger army does not only mean that you get more options when it comes to dealing with your opponent, it also means that you might be able to field more of the big and point expensive pieces in your army that otherwise would not get to see any light on the table (lords riding monsters, a really killy character, a powerful wizard that does not have to be your general, etc). It also means that most unit sizes has to swell in order to withstand the increased heat, which in turn makes smaller sized units a less viable playstyle. It opens up various playstyles and strategies, and shuts down others, compared to playing with 2000pts.
But, in my opinion, playing 2,5k-3k armies is more beneficial for some armies than others since it increases the chance of introducing characters or units that the opponent can't find a way to counter. Sure, I can bring another cannon with the extra points to counter that shiny dragon - but the increased point limit also meant that my opponent get to field a unit that will hunt my artillery. One player's solution becomes the other player's problem, which will require a solution from the first player again, etc. That counter cycle will of course always be there no matter the point costs, but at higher point games I have found that the leap between the balance of finding solutions to the problems becomes wider.
I think in your case it is about clashing player mentalities. It sounds like your opponents wants to field all of their toys in one big battle while your side that is more used to playing in the spirit of 6th edition wants another type of game to play out. Maybe you all can discuss what kind of playing experience you all are after and either find a compromise - or maybe both sides can try each other's way to play. Maybe even see if they can be introduced to a game of 6th edition so you all can compare it to playing a game of 8th with 3000 points?
Also (as a sidenote), I have experienced similar gripes from opponents that after a game goes: "Yes I lost, but if I just would have had this other tool that I could not afford in this list I would have won this game". Firstly, who cares about who wins, really? Both players are there to enjoy the hobby together and have a good time so it is best to just see the game as a narrative that plays out that both players help come to life rather than seeing the game as an outlet to "win" over an opponent. Secondly, building a list while restricted to a point limit it part of the list building process and an important part of the game. The list is all about giving yourself the tools needed to counter the opponents list (if possible), and if one list finds a way to counter the other then so it may be. To be saying "oh I would have won if we played with bigger armies because then I could afford this other nifty tool to counter your current list" is to me like playing the game "rock, paper, scissors" and complaining about not getting to use the rock after having played the paper against the scissor.
To, as you put it, make 8th edition manifest in all its glory I think it is important to talk with one's opponents and come to an understanding what kind of experience you all are after. Is it big monsters, big blocks, and so on? Great, play 2,5k or even 3k armies. If it is something more akin to the spirit of 6th edition, play a smaller point game to negate the devestating key elements of 8th. Playing a smaller game does not negate the inbalance of 8th edition though, and in some ways (like playing below 2k) could make it even worse.
Lastly, what about trying to play a 3k or 4k all together - but every side brings smaller armies that plays as allies? So in a 4k game there could be four 1k armies or two 2k armies. It would not enable the players that love big and expensive center pieces to play with their prefered toys, but it would allow a big and eye-pleasing game with lots of miniatures on the table. It would also bring out interesting matchups of allies when different armies can bring their synergies to one another. Dwarfs marching alongside the Empire to gain access to magic and buffs from imperial wizards and wagons could be a nice fit, for example.