Tech Advances seem to make a pretty substantial difference, but there are a LOT of techs and you won't get too many of them so you have to be very picky.
Some examples in my recent game as Prussia:
Prussia has powerful Artillery and all the resources needed to make a LOT of artillery units. It also has a well disceplined army (makes it easy to do Line formation).
I had to pick from over a dozen techs, but three of them were of interest:
Massed Artillery (+25% artillery damage)
Double Line Formation (+33% damage when in line formation at the cost of -2 mobility)
or Colonial Warfare (10% chance to capture enemy colonies when at war).
Colonial Warfare made the list because I was sadly at war with 4 opponents. This means I would have had a 40% chance to capture a colony every turn. Colonies provide a couple benefits. 1 gold/turn, 1/10th spice per turn (1 spice for every 10), and if you have Colonial Militia tech 1 militia for every 10 or 20 colonies. Mind you, militia suck horribly at anything except defending forts... but they have some good uses such as using them to help flank enemies, placing them inside forts in detailed battle (they get to act as Artillery), or just holding out in a fort until real help arrives.
In the end I picked Massed Artillery, it was a bad choice because I was too busy fighting to have enough time to build up a powerfull artillery division. Should have taken double line...
Oh well :-)
On the issue of if a single unit can dominate the game... No, they really can't. I effectively used a cavalry only army as Spain, but never did I go into battle ONLY with my cavalry, it was always backed by an infantry/artillery combo. Every unit has drawbacks, cavalry is no exception, here's how you would beat any "X-unit only" army:
Cavalry: Use high numbers of Infantry. Cavalry are poor at firing combat and great at charging, but charging is very dangerous and causes disorgnization. If you use your infantry right you force the cavarly to charge a well formed army (square or line) front the front (or at least the side). The cavalry will hurt themselves as much as you AND be disordered. You can then surround them entirely with your large quantity of infantry and simply slay them at your leisure. Keep in mind this also results in cavalry surrendering, which gives you 50 horses to build your OWN army with.
Artillery: Anyone dumb enough to have an artillery only army is in great peril. Artillery go down very easy to Cavalry and infantry charges. Once you defeat an artillery (or it surrenders) it comes under your control, which means if someone attacked with only super-power artillery you'd have one nice super-artillery army for your own use very quickly.
Infantry: An infantry only army is a tough nut to crack but the proper use of any well designed army will beat them. Use artillery at range to inflict horrible casualties (between 200-500 per volly) and break their formation while your infantry keeps them pinned down (and tries to break their formation as well). Then once they are disordered send in the cavalry and charge them for a whopping between 500 and 5000 (depending on many conditions) casualties.
Obviously none of this is true if there are like 2x as many units as you have, but in an even battle a well organized and mixed army should prevail. You should still focus tech on what will make you toughest. An infantry only army with double line formation and guards is going to be tough to kill... :)