Lets say in battle I have two groups of archers, or swordsmen. One group has 20 in, and one group has only 3. Is the group with 20 harder for the enemy to kill? How does the game handle this? Am I smarter to have groups with many soldiers in them, or few?

Let's say an enemy stack attacks and does 100 damage. Let's say an individual swordsman has 20 health. The enemy attack will kill 5 swordsmen, regardless of how many are in the stack. If there are 5 or less swordsmen in the stack then the stack is destroyed, while if there are more then the number in the stack is reduced by the number that were killed.
In terms of overall tactics, splitting a group into multiple stacks can be useful if as a single stack that unit is one-shotting enemy stacks and doing far more damage than is necessary to kill the stack, as in this case damage is being wasted and splitting the units would still likely allow you to one-shot enemy stacks, but now you've got two unit stacks that can do this each round rather than just one. However, most of the time it will be better to keep each unit type as a single stack so that you can get the maximum number of units possible in your army.

Thanks for the explanation. I assume the offensive side of things is handles the same way? As in, how much damage does a group of 3 soldiers do vs a group of 20?

Pretty much. The damage that each unit does is simply multiplied by however many units are in the stack (well, then attack and defense skills are factored in, but that gets into more complicated calculations).

Great - thanks again!

Most of the time, keep only one stack.
Let's take a stack of 20 enemies that can kill 20 of your guys per attack (one per person). Let's suppose every 10 of you guy can kill one of their. Suppose you have 100 dudes. Enemy has initiative.
ONE STACK
If you have one big stack of 100, the enemy attacks first and kills 20 of your guys. Your guys ripost, you kill 8 of them. Then you attack, you kill 8 more. They ripost, they kill 4 guys.
Lost : 24
Killed : 16
TWO STACKS
The enemy attack one of your stack, you lose 20 and kill 3. Then you attack, you kill 5 and lost 12, then kill 3
Lost : 32
Killed : 11
It is only useful to have several stacks in the following circumstances :
- The unit can cast (non-damage) spells, for instance a buff. You might want to separate a small number of units while the others attack.
- The unit is fast, you might want to separate the stack to be able to "occupy" two stacks of archers instead of one
- You have REALLY a lot of units, and wants to avoid blind or other crippling spells, or avoid to waste damage (rarely an issue in this case).

Lots of ranged opponents can make separating stacks a great idea.
They are also good when you want to have one weak or expendable stack eat up the retaliations each round while the other stack keeps hitting at full unit strength all through a fight. Split off some of those dwarfs so they get retaliated against instead of your dragons, and it could make the difference between winning or losing the battle.