As a personal opinion (an a faintly jingoistic Brit) Wellington was a genius with what he had – HIS choice of battlefield, French generals who would launch an assault on his chosen position and infantry that HE could rely on.
1. He could practically guarantee a battle with any French general by choosing merely to stay in one place. My reasoning – every battle he won added to his "invincible" myth and any French general would be both honour bound to destroy him for the good of France and also to enhance his personal Kudos for been the man that broke Wellington. He did this to Napoleon at Waterloo – he chose his ground and Napoleon came to him.
2. He knew how devastating artillery could be so his chosen battlefields (and he DID choose most of them – see point 1) normally had his troops in some form of cover, even if it was just a small dip, a road cutting or lip of a hill. This makes a lot of difference if most artillery fire is line of sight.
3. He knew (especially in Spain) that the French would launch an immediate assault and not wait him out simply because because the French supply system was basically "eat this area bare then move or starve". His supplies meant he could stay in one place for as long as he wanted.
4. He knew that his British troops, especially his infantry, wouldn't rout. Not because of pride, hubris or some mystical belief but history. British troops under a commander they respect fight hard. An example would be Neerwinden in 1693. The allied army was been crushed and forced to retreat in haste (somewhere between a rout and a retreat) and an English regiment in the rear guard captured a French standard. Hard enough if your winning but nigh impossible if your losing. Another example (though not for Wellington) would be Inkerman 1854. They didn't even have a general but they held.
I don't know if he could have fought in the "European" style moving massive columns of troops around a battlefield because his chosen strategy never required him to. Probably not since he no reason to learn to.
His strategy worked well enough – advance slowly through a country ensuring good supply lines (mainly by not giving the locals reason to go guerilla – his army was under STRICT orders to PAY for everything they wanted – during his advance through France in 1814, French civilians never quite got used find redcoats hung at crossroads for looting a country they were at war with), choose good defensive ground and then wait for the French to attack, which they would because they HAD to destroy him.
I'd like to point out that the French forces opposing him while not the elite weren't bottom of the barrel either. They were average soldiers. On top of this their generals were above average compared to most European armies simply because the French army was almost a meritocracy. You had to be fairly good to be promoted.
Instead of judging Wellington on HIS merits, judge him on his ENEMIES merits. He defeated some good generals so he must have been fairly good himself.
It's been mentioned that the British army was an 18th century army in a Napoleonic world. I would heartily agree with this but I'll start a new post. This ones too long.