As a designer I would say, fixed. It's a very elegant solution.

As a designer that wants to sell his games I say go for random range.

As a player that wants to have fun I definitely say go for random range.

Someone above mentioned Diplomacy and Risk. Yes, Diplomacy is an awesome game, no doubt. But compare how popular the Risk is and how popular Diplomacy is. Sure, you can say that brainless casuals play Risk (which is actually partially true :D), but I feel there is more to it. I would not discard randomness too quickly.

Wow. Some really great stuff guys. I like the idea of a slight variance possibly being the difference between a unit living or dying, whereas set damage would cause the unit to live or die every time. I also feel that the variance should be relatively small to enable this situation occasionally, but not large enough to win battles based on luck. Due to this I have come up with a new damage formula. I added some unit advantages for more variance and strategic reasons.

Base unit damage * (95%-105%) * field location bonus/penalty * strategic points controlled bonus * slight total number of allies bonus

The field location bonus is based on terrain and where the fight is occurring on the battlefield. Strategic points are areas on the battlefield that a team can capture to generate bonuses for their units, and the number of allies bonus is a partial solution to my number of units on screen at a time problem. (I can only support so many units so I have a reserve system. The current units on the field get a slight morale bonus based on the number of reserves available.)

With all of the variance do you think I even need the 95%-105% randomness?

I like that morale system. Basing it on reserves is pretty cool, and gives some incentive towards not keeping the field flooded as much as possible at all times.

Whether or not that randomness has any real impact depends upon, again, the pace of your battles and how important each unit is. Without knowing more, I can only recommend playtesting it - it's a simple element to remove, at any rate.

Also, I'll mention that when I include randomness into things like damage calculation I tend to go with a normal distrubution - that is to say, damage is centered around a particular mean (the unit's base damage value) and rarely deviate by much.

randomness is a fact of life in combat, and should be modeled to the degree necessary for whatever level of realism you're aiming for in your combat simulation. as mentioned elsewhere in this thread, the frequency distribution of the random values generated must be sufficiently realistic as well. so if you're shooting for a high degree of realism you should model things like random damage, friendly fire, tripping, morale, weapon breakage, etc.

in my caveman sim/rpg, chance to hit, damage done, chance to flee (morale), opponent hit points, and weapon wear and tear and breakage all have some randomness to them.