What does changing the leader hero's race do in Age of Wonders I (if anything)?

Wow, it does change things

Depending on your chosen race, you get different starting stats and skills. At the start all of the leaders get Spellcasting I, Strike, and Walking, and have 10 HP. Stats of different races, Attack/Defence/Damage/Resistance/Movement points, then the total cost of things taken in skill points (if everything was to be raised to this level from 0) are:

• Elves: 3/3/3/3/36, 147 points, Forestry (5), 152 total.

• Dwarves: 3/3/4/4/32, 154 points, Cave Crawling (5) and Mountaineering (5), 164 points totally.

• Halflings: 3/3/3/4/32, 144 points, no special skills.

• Dark Elves: 3/2/3/5/36, 152 points, Night Vision (5), 157 totally.

• Orcs: 3/3/4/3/36, 157 points, Night Vision (5), 162 totally

• Goblins: 3/3/3/2/32, 134 points, Night Vision (5), Cave Crawling (5), 144 points totally.

• Lizardmen: 3/3/3/2/32, Swimming (unknown, not available at the start for other races, so invaluable for the moment), 134 total+Swimming

• Azracs: 4/2/3/3/36, Fire Protection (5), 152 points.

It turns out that on the...

Good side:

• Halflings are actively bad. They have nothing strong at all. Bad in the long run, bad at the start. No reason to choose Halfling commander. I have yet to check the claim that the Halfling commander is able to buy Hurl Stones after chargen. If true, this may allow for some interesting builds
• Dwarves have good starting specials, but are rather slow. You would like to increase their move points at the first level-up if not from the start.
• Elves are not as awesome for a striker hero as Dwarves, and their special is not that good. But they have higher starting move points, so in campaigns you can invest all of their 25 starting bonus skill points into some interesting abilities.
• Lizards are useless unless the map has a lot of water, as usual with Lizardmen. They are the weakest among everyone. Even on water maps, their usefulness is questionable.
• Azracs make weaker fighters than Dwarves, and a bit weaker non-fighters than Elves due to Defence being a bit lower. If you really need Fire Protection, you can go for them.

On the Evil side:

• Orcs, with their increased Damage, Defence, and full movement, make better fighters, far better than Dwarves on the Good side due to bigger movement.
• Dark Elves, even with their Resistance of 5, are inferior to Orcs.
• Goblins are just weak, no reason to take them as a leader.
• Lizardmen are just as weak as before. Probably only take if there's a lot of water.
• Azracs are weaker than Orcs in pretty much any role.

So: Go for Dwarves as fighters on the Good side, for Elves as other roles, on the Evil side go for Orcs as fighters and for Dark Elves as other roles. You will hardly make a mistake if you forget everyone else, at least if you are just starting to learn AoW 1.

Other races do exist in the game, but I didn't check their stats yet.

I didn't check if the list of available skills depends on the race, but it's worth checking.