In my group we couldn't be bothered in session 1 to look up if the attacker needed to score equal to or greater than the defender's AC in order to hit. We decided to live in a 'defensive' world, and ruled "Defender wins ties." This goes both ways for PC's and NPC's/Monsters alike.

We've played like this for months and I've been wondering just how much this throws off, if at all, encounter difficulty. Is there a specific AC threshold in DnD5e that is thrown off by this? Does this favor 'horde' encounters or 'lone boss' encounters in some way?

I understand these are sub-questions but they are so closely tied to the central question I don't feel they should be separated.

This has very minimal impact on CR math

The easiest way to evaluate the impact of these changes is to evaluate how they impact CR based on the suggested guidelines for calculating CR for a custom creature.

From the Dungeon Master's Guide, Chapter 9 ("Dungeon Master's Workshop"), subsection "Creating a Monster", the following guideline is given for adjusting the CR of a creature, for Armor Class:

Now look at the Armor Class suggested for a monster of that challenge rating. If your monster's AC is at least two points higher or lower than that number, adjust the challenge rating suggested by its hit points up or down by 1 for every 2 points of difference.

Because every single creature is having its AC increased by 1 with no other changes, this is equivalent to all creatures having their Defensive CR increased by 1/2.

The guidelines for Attack Bonuses are similar:

Now look at the attack bonus suggested for a monster of that challenge rating. If your monster's attack bonus is at least two points higher or lower than that number, adjust the challenge rating suggested by its damage output up or down by 1 for every 2 points of difference.

In the same way, this means the Offensive CR of attack-roll-based creatures has decreased by 1/2. Creatures that depend on Saving Throws for most of their damage won't see an Offensive CR change.

So for all creatures, Defensive CR is being increased by 1/2, and for attack-roll creatures, Offensive CR is being decreased by 1/2, with Saving-Throw creatures seeing no reduction in Offensive CR. For the former creatures, short of especially esoteric situations, the net impact of these changes is not likely to change a creature's overall CR. For the latter, a change of 1/4CR (averaging +1/2 and +0) may be significant at lower levels of play, but is unlikely to impact anything beyond the first few levels of play.

Impact on overall game balance

Battles are going to take slightly longer than usual. All creatures are going to hit with attacks slightly less frequently, which will mean that overall, they take less damage than usual. Healing becomes slightly more powerful under this ruleset, because damage totals are lower, which means healing represents a larger proportion of damage issued during a fight.

Damage will become slightly more swingy, with characters staying at their same level of Hitpoints for longer than usual.

Players (generally) benefit from this system more than hostile creatures

This mostly boils down to the happenstance of how damage sources work. Players are more likely to depend on Spells or Saving-Throw-based Cantrips than hostile creatures are, and Saving Throws are unaffected by these changes (being already "Defender Wins" as written). So those spells will stay at the same power level, whereas weapon attacks and Attack-Roll-based spells (which are more common among hostile creatures) will be negatively affected.

I would say no change to CR.

There is an (approximate) 5% chance that a given roll ties with defender AC. If 5% of attacks DON'T land, for monsters and players alike, I think the game will remain largely the same.

In effect this increases AC of all things by 1, if you were playing "meets beats". Which I don't think is relevant for any single encounter/monster... But a players AC is tested over a larger period of time than one encounter.

A better way to look at this might be "What is the effect of that one extra point of AC, for everything". Looking that up brought me to this post on Reddit. I duplicated the spreadsheet linked within, increased all the armor AC values by 1, and saw that got me. You can try this yourself to look at the differences, but the general results are the same. Enemy hit chance is 5% to 3% lower across basically all levels and AC's, and DPR is slightly lower in all categories as well, but trends are the same across both sheets, leading me to believe that all this has done is make everything, players and monsters alike, a little more durable.

After writing that last sentence I wasn't satisfied so I went searching for DPR tables for players and found this gem. Repeating the same "increase all enemy AC by 1" trick I did with the last sheet and checking results, I noticed that changes in KPR and DPR were no more significant, but did change trends between sheets slightly, although I would be hard pressed to break that down for you in a way has a concrete answer. Looks like KPR for all classes and breakdowns in that table dropped somewhere from 1% - 4%... Except Sword and Board Barbarian, which stayed exactly the same.

Which means everything is harder to kill, and has a harder time killing everything else. Except S&B Barbs. Do you have one in your party?