The biggest two advances that separate these two forces are the armour and the stirrup.

First, the armour. Macedonian infantry armour at this time would be a large shield called the hoplon, chest armour, either made out of leather or bronze, and likely both greaves and bracers (possibly only on their weapon arm). Their helm would bronze, and likely in the Boeotian style which was basically a skullcap. Cavalry was likely similarly equipped, although companion cavalry did not normally carry a shield as they were lancers. How does this compare to the Crusaders? Pretty poorly. Crusaders were, for starters, generally wearing much heavier armour. At the very least this was a full mail coat, including coverings for their arms and most likely good protection below the waist. Helms wouldn't be the fully enclosed type most likely yet, but both they and the body armour would be steel rather than bronze. In terms of cavalry, armour would be very similar, particularly protecting the flanks of the body better, and carrying a shield almost certainly. The fully armoured cavalry was still a ways off from filtering into Western Europe, but they were around at this time in the East.

Now, there is no doubt that one on one, the heavy armour of the medieval warrior was going to be a pretty big advantage, and definitely represents a significant advance, particularly materially as the armour was going to be more sturdy in addition to covering more. It should be noted though that not every foot soldier was so well equipped. Lighter archers and crossbow men wouldn't be wearing nearly so much protection. However, the best armed and armoured crusaders were a lot more well protected than the best Macedonian ones.

Now, there is the other piece of the puzzle, the stirrup. This piece of technology gives a heavy cavalry man more stability, and particularly, more control over the horse. Dismounting a soldier from a horse without a stirrup is much easier, and in general the stirrup helped greatly in securing the role of heavy cavalry. Without it, Alexander's companions would be at a distinct disadvantage.

So, in short, the main advances were in armour design and material, and the stirrup.

The two huge differences would be saddle and stirrup and armor. The weapons they used would be different as well as different armor would render certain weapons less than effective.

The infantry of Alexander would wear lino-thorax or linen armor. Its fairly effective against missiles, light and cheep. They'd be topped with a bronze helmet that covered their whole head. The Eastern Empire at this time would have used a hoplite style system with close formations of heavily armored infantry with large shields and spears. The Frankish Crusaders would be a bit less organized with soldiers using anything from shield and spear to large danish axes and anything in between. They were much more of a hodge podge. The thing is though the 12th century solider would if he could have chain mail which is highly effective against slashing weapons like the kopis that the Macedonian soldiers would have. Head on against a pike phalanx it wouldn't really matter.

What really makes Alexanders army, infective against the 12th century army would be the saddle and stirrup. Alexander more or less rode his horse bareback. which means they held their lances overhand and stabbed with them. The amount of thrust could not break the armor or unhorse a cataphract or a heavy mounted knight. A 12th century knight would be mounted in a high backed saddle with stirrups which would allow them to couch their lance (hold it under their arm) and put the whole weight of the horse and soldier to bear down on that target. The knights would be wholly more effective than Alexanders companions.

Man to man i think Alexanders men could give them a run for their money. However Alexander in all his set piece battles used really only one tactic which was set the infantry in the center cavalry on both wings. Have the left wing feint and the right wing deliver the crushing blow while the infantry was engaged. Could Alexander beat a crusader army in the feild? Ya its possible, Alexander did have more men at Gaugamela than the combined Roman Crusader force at Nicaea. Alexanders men were also highly trained veterans while the Crusaders were like 50/50 trained knights and men at arms along with peasant rabble.

So to answer your question, The infantry would be pretty similar with a slight edge to the equipment to the 12th century man. The cavalry, However; there would be a huge disparity with a overwhelming superiority to the 12th century.

How would Roman armies compare to medieval? They're equipped with metal armour, unlike Alexander's armies. Would the cavalry difference still make or break it?