Lets begin by looking at a list of the best civs to worst. Note this is roughly based on Andes in and out of natives.
Now every civ should beat the civ above them for a specific reason. The op civs win for obvious reasons, and I would prefer not to get into them.
Spain vs Spain. Get ready for an extremely fast game. Lancer/Nat/Huss/Skirm, or Lancer/nat/skirm/rod, Depending on what your opponent makes, you can switch between the two compositions. If your opponent is going heavy on lancers skirm, no rods, and just natives, adding hussar into your mix can counter this well, however this is directly countered by someone making a considerable amount of rods with lancer/skirm/nat. And this can be directly countered by pure skirm/lancer/nat, thus starting at the begining again.
Spain vs Iroquois. Spain wins this match up hard because their military dominate Iroquois. Eco is not a main factor in this MU. Spain plays Skirm/Natives and heavy on Lancers with some culvs out at all times to deal with Light cannons. As well as a few mortars while pushing. Iroquois military is primarily Skirm/Native/Mantlet/LC, so heavy lancers will force the Iro to produce less cost effective ways of dealing with them, such as Tomahawks or Musket riders, which easily gets countered by Spain Skirms and natives anyway. MU is almost never played outside of cliffs.
Spain vs Germans. Spain is superior in this MU because their military is far too good for Germans to battle, and this MU usually ends up in a 1.5 K/D for Spain. Spain can play this MU in a few ways. I personally found that a large skirm base works exceedingly well against Germans sub par anti inf units. However they can also go their traditional Skirm\Lancer\Native, this however can give the German some chances, regardless, Spain should win either way. Outside of cliffs Spain wins this MU even harder, Germans now don't have as effective anti cav, therefore lancer/skirm/rod can be very effective.
Spain vs British. Spain wins this because British don't have an effective way to hold them. Either the British will go Musk/Native/Hussar, which is insanely Food heavy, and they can't support this very well, or they go a longbow/native/musk with some huss composition, which in turn can be pushed very easily by Lancer/Nat/Skirm/culv, and some rods. Out of cliffs, British will have more of a chance against Lancer/Rod/Skirm/culv with musk/huss and heavy on art.
Spain vs Portuguese. Spain should win this MU because Ports military and
economy doesn't mix as well with Natives. In addition, Spains' military
is far superior because Ports best units, Dragoon/Cass and even musk
are countered hard by rod/lancer/skirm or native/lancer skirm. Be weary
though, Ports can stand a chance if they mega camp art.
Spain vs India. Spain win this insanely hard because India can't support natives for jack sh*t. Outside of the cliffs, India can always win by running, which Spain is weak to.
Spain vs Sioux. Sioux lose this because Spains' military and eco are superior. Just like any civ vs Sioux, skirm/mort/walls will win.
Spain vs Dutch. Spain wins against Dutch's sub par eco and military. In cliff, Spain will dominate with lancer/skirm/nat/ and decent amount of culv. Outside Dutch can stand a bit more of a chance by camping art, but should still get dominated by a larger skirm mass with some lancer/rod and a generous amount of culv.
Spain vs Aztecs. Retarded MU, should never be played, not even vs conscripts. Spain wins with a large amount of skirm/natives/mort. Only chance for Aztecs is to win by getting complete map control with their 320 pop start army and running invisible jags into spains base. Yes cheese strats from the aztec are fine to do in this MU since you're at such a large disadvantage.
Spain vs Ottomans. Spain wins easy, Ottomans can't compete with Lancer/Native/Skirm effectively because their train times for jans is to long. Jan/native and camp art with a few huss to block lancer in between jan batches is their only hope. Abus are bad in this MU. Spain should be able to push the slow ottoman train times with ease.
Iroquois vs Iroquois. Basic composition of Mantlet/ForestProwler/LC, some natives if you want to push. Basically what I think determines this MU is Light Cannon Micro, and effective macroing use of your firepit and cows. Then again I've only played this MU once competitively against Fuher. :P
Iroquois vs Germans. Quite the opposite of Spain vs Iroquois. Germans lose this MU because their military doesn't fair well against Iroquois, in addition, Iroquois economy is far superior to Germans. Iroquois can play very Skirm heavy with no more than 10 LC and 15 Mantlet in the MU and the German wont be able to count effectively at all because their skirms and Uhlans are Sub par, and their eco is a joke compared to Iroquois.
Iroquois vs British. A difficult MU for the British since they can't effectively stop an Iroquois Skirm/Mantlet/LC/Native push. British will either drain from a large amount of hussars/natives/longbows, or get WTFPUSHED because longbows don't do well against Iro units. MU isn't played outside of the cliffs.
Iroquois vs Portuguese. Regardless of Ports very good Skirms, and artillery, they don't stand much chance against Iroquois because their eco doesn't support natives very well. Even when not using natives port can't compete with Iroquois large mass of Natives/Skirm/Mantlet and deal with LC. Best chance for Portuguese is to either try to camp art, or hope your opponent gets map screwed cliffs, send long range mortars before 40, and keep him off the posts. This can work for any civ of course.
Iroquois vs India. One of the most unfair MU's in the game, siege eles can't deal with 32 ranged LC at all, nor can mahout with their awful pathing issues, they will just get blocked by mantlets and natives. Best thing India can do it flank around his native posts somehow and build behind, then flank the Iro's forward base, causing him to further more split his attention. Running isn't going to work too well because 5 LC behind some walls will stop any means of India trying to get through walls with siege eles.
Iroquois vs Sioux. I'll leave this for someone else to answer, since I've never seen this played, or even heard of this MU being played.
Iroquois vs Dutch. Iroquois can just go their basic Composition, but instead go a little more skirm heavy, and less light cannons. Dutch's skirms stand no chance of cost effectively combating with Forest Prowlers. But they can deal with a large amount of artillery. Dutch can go a large amount of horse art and culvs and try to camp the Iro out of wood, but it most likely wont happen.
Iroquois vs Aztec. Complete one sided bash. Iroquois will roll them with a basic composition. Best thing an Aztec could do it 2 vs 1 the Iro and get your teammate to help fight the light cannons.
Iroquois vs Ottomans. Pure Abus/culv/native is the most cost effective composition for the Ottoman. Hussar spam at the start and make a few mortars to try to pressure his native posts. If this fails, try to stall the Iro out of wood with Abus/Native/Culv. Iroquois can do their Skirm/Nat/Mantlet with a good amount of LC, this will cause the ottoman to produce culvs, which will decrease their Abus mass giving you a pushing advantage.
Imma edit in more later