[Saber Cherry]

AIs will not attack you unless you attack them, or they declare war. Normally, they will not declare war unless you look weak. You can prevent yourself from looking weak by keeping your province defense on border provinces at 10+ (the higher the better, I think) and probably putting some units there too. I'm sure there are other factors as well, but I forget them.

The difference between Dominions and the other games you mentioned (I've played all of them, except AoW2:SM) is the the other games don't have magic, or don't require magic to win. You can win an easy game of Dominions (1-on-1 versus an AI) using troop strength, but to win a game versus multiple AIs or any multiplayer game, you will have to focus on a magical strategy (or, sometimes, a heavy bless strategy, but I'll ignore that for now). This means spending a substantial amount of money on research mages, possibly doing a lot of site-searching, forging some magical-path-boosting items like Thistle Mace, Earth Boots, or Skull Staff, and aiming your research toward specific spells. For example, if you did site-searching and found a magic site that lets you recruit Fire-3 mages, you would want to research Phoenix Power and Falling Fires, and buy one of those mages every turn until you can incinerate enemy armies before they get close enough to land a blow. But if you were Man (which has good archers) and found that site, maybe you would just spend money on archers, and cast flaming arrows (needing only one mage for the whole army), then annihilate the enemy.

If you ever play in multiplayer and field an immense army of Hoplites against an enemy (say, Vanheim) army a quarter of your size, you might be shocked to lose. Watching the replay, you might notice that 10% of your army routed or died from scary False Horrors, which are free battle summons; your entire peltast support wing was killed by Blade Wind; and the remaining 70% died in combat with inferior soldiers, because they had Fog Warriors (+mistform: nonmagical attacks usually do 1 damage), Weapons of Sharpness (+armor piercing), and Legions of Steel (+3 protection) while your troops were unbuffed.

Alternately, you would literally be shocked to lose to a lone Vanherse wielding a Staff of Storms, who casts Shimmering Fields for ~10 damage (armor negating) over area ~50 (which would be 150 hoplites, if they were packed).

In other words... play around with the spells. Flying Stones and Fireflies are not representative of their big brothers, Gifts from Heaven and Firestorm.