Basic D&D has different Dex modifiers to AC, and different entries for armors worse than chain. The combination can result in up to a 2 point AC difference.
Note that AD&D2E has the same AC's as 1E, but has more armors; I've put the ones not in 1E PH in (parentheses).
_____________________ Armor for a given AC _______________________
AC Basic Advanced D&D 1E (2E) Labyrinth Lord
10 --- . . . . . . None . . . . . . . . . . . . . . ---
9 No Armor . . . Shield Only . . . . . . . . . . Unarmored
8 Shield Only . . Leather/Padded . . . . . . . . . Padded, Leather
7 Leather . . . . Studded Leather, Ring Mail . . . Studded Leather
6 Scale Mail . . Scale, (Brigandine, Hide) . . . Scale Mail
5 Chain Mail . . Chain Mail . . . . . . . . . . . Chain Mail
4 Banded Mail . . Banded, Splint, (Bronze Plate) . Banded,Splint
3 Plate Mail . . Plate Mail . . . . . . . . . . . Plate Mail
2 --- . . . . . . (Field Plate) . . . . . . . . . ---
1 --- . . . . . . (Full Plate) . . . . . . . . . . ---
0 Suit Armor . . --- . . . . . . . . . . . . . . ---
AC Dex Adjustment
Dex: 3 4 5 6 7-8 9-12 13-14 15 16 17 18-19 20-21 22-23
Basic D&D: +3 +2 +2 +1 +1 +0 -1 -1 -2 -2 -3 -4 -5
Advanced D&D 1: +4 +3 +2 +1 +0 +0 +0 -1 -2 -3 -4 -- --
Advanced D&D 2: +4 +3 +2 +1 +0 +0 +0 -1 -2 -3 -4 -5 -6
Labyrinth Ld: +3 +2 +2 +1 +1 +0 -1 -1 -2 -2 -3 -- --
For monsters, you won't need to adjust at all. For characters, if AC is 6 or higher, you may want to adjust it.
References:
TSR2010 AD&D1E Player's Handbook, 6th printing, ©1980.
TSR2101 AD&D2E Player's Handbook Electronic Edition (from Core Rules 2.0 CD)
TSR1071 D&D Rules Cyclopedia Scanned/OCR'd Edition (From DTRPG)
GBD1001 Labyrinth Lord (No Art, via DTRPG.)
Edit Note: I added the LL data in for completeness.
If combat is a more minor element of your adventures then using narrative combat can keep the game flowing in the same manner as other types of encounters rather than switching to a separate type of "mini game". If combat is the major element of your game the greater tactical options of using miniatures can be more enjoyable to a lot of players.
It really depends on what aspects of the game you and your group find the most important.
Best Answer
Yes, you simply make it up. The trick is that you not only have to make it all up but keep it consistent and communicate it all clearly to your players. They have to be able to visualize the whole setup of a scene: where everyone is, what objects are there, what opportunities and/or hindrances those objects (may) present to them, what they see, what they hear, smell, and so on (because visually hidden stuff might be hinted at by the other senses, obviously.)
Of course, at the same time, you have to keep it balanced to avoid bogging down your game with listing countless irrelevant details. You'll have to establish a common understanding with the party, learn what your players know about the setting (or its inspiring real-life era and setting), and bring everyone to an equal level... so that when you say "it's an average innhouse" everyone knows what that implies in your world (a stove or two? a fireplace? a bar, or proper tables, or just barrels cut in half, turned upside down for both tables and seating? a few waitresses? barmaids? an innkeeper? lots of large windows, or just a few holes in a several feet wide wall?) ...and so on. Do draw their attention to what's important, what's unusual, sum everything else up, and allow player input based on assumed information (for example, if you haven't mentioned that there's a cellar, but someone assumes there's one, because all the inns they've ever visited had one, let this inn have one as well, and the next time when there isn't one, mention that explicitly.)
Imagine the scene, and communicate it briefly and effectively. If necessary, update your players round by round about the meaningful and important changes taking place -- again, briefly (in a short sentence or two) and effectively. Use your descriptions to establish mood as well -- as that may even influence combat.