So, how "off" are the level-appropriate encounters? I tend to have trouble (or HAD trouble in 3E and PF) when I follow the level-appropriate encounter rules with my powergaming PCs.
Off enough to make CR almost irrelevant. In particular, the CR-assignment guidelines basically ignore everything but HP and damage rates: special abilities get translated into boosts to effective HP/damage and then that is used to compute the CR. Disguises, movement and ranged combat are particularly undervalued except, oddly enough, by low-level monsters like orcs (Aggressive trait helps a lot) and (hob)goblins (decent DX, long-ranged weapons). Teleport is a
free ability for monsters, for example: it doesn't affect CR at all! CR appears to be built under the default assumption that all monsters will charge directly into melee with all the PCs and hammer away at each other under one side falls down. Thus, it scales pretty linearly in HP/damage.
There are CR 5 monsters that I would gladly take on solo as a 1st level character, just for the XP. And there are CR 2 monsters that I would avoid like the plague even at level 10 because the risk/reward ratio is just not there.
If you have players who are tactically-minded and took abilities which let them control the pace of combat and the engagement range (Mobile feat, Longstrider, Expeditious Retreat, etc.), you can and should pretty much ignore CR guidelines for any combat where the PCs are not ambushed at melee range. I mentioned throwing 80,000 XP worth of enemies at my 3rd level PCs, right? It was touch and go until they took out the enemy spellcaster with Fireball, but exploiting surprise, terrain and ranged weaponry was enough to win the battle. (They didn't kill them all to death either; they were smart enough to mostly ignore the Umber Hulks and focus on killing the Neogis, on the assumption that once the masters were dead the slaves would lose their motivation.)
Of course, after that battle, they are no longer 3rd level PCs.
I think 5E works best from an AD&D mindset of "there's as many monsters as there are, now what are you going to do about it" instead of a 3E mindset of "the DM will give you level-appropriate encounters." I skipped 3E except for in video games, but from Internet forums I get the idea that 3E players expect "fair" challenges calibrated to PC level.