Here's a very 'poor' rough draft on the civ's and their tiers. It's 'poor' as I can't take everything into the model.
I'll also give/subtract points based upon settings. That way, you can move up or down the list based upon the speed of the game.
edit: rescaling to a 1-5 scale. Only the top few UA, UU, UB, UT will get +5. the rest will be lower. Will mean that the UT's and UB's are compared against each other.
edit 2: rescaling UAs to a 1-10 scale given their power, or not, across the whole game compared to UU/UB/UGP/UT. (5 is avg, after that, it'll go up or down compared to others; not having it = 0)
E/M = Epic/Marathon; Q = Quick; S = Standard
France (+14<->+12)
UA - E/M +8 Q/S +6 (not situational, good early-mid game - drives faster deep SP grabs, but has an end point)
UU1 (Musket) - situational: E/M +3, Q/S +1 (will be outdated within 2 techs, nothing special about it upgrades)
UU2 (Foreign Legions) - +3 (not situational, late game unit; but can be built for promo then upgraded to mech)
Persia (+16<->+14)
UA - +9 (not situational, good all game, two useful bonuses in one)
UB - +4 (always built, happiness bonus = city unhappiness = more GAs; see UA)
UU - situational E/M +3, Q +1, S +2 (early game rusher, double heal = less losses, costly upgrade path)
Siam (+17<->+14)
UA - situational If CSs/used well +8, else +5 (great SP/Patronage synergy, good all game, can be useless if no CSs/few used)
UB - +5 (always built, can be Legalism gained, no libraries needed)
UU - +4 (no resources and will work until Industrial Era units, game speed doesn't matter)
Songhai (+14<->+12)
UA - +8 (two bonuses, both useful. useful all game if you're fighting all game)
UB - +3 (legalism chooses it first, no cost, culture only building)
UU - situational E/M +3, Q +1, S +2 (melee knight replacement, direct upgrade makes the unit worse than before upgrading)
Babylon (+17<->+13)
UA - +10 (useful all game, science bonus x 2)
UB - situational +4 E/M, Q = 2, S = +3 (higher defense walls with + RA, mixes with SPs if needed; on quicker speeds pace of unit power/bombardments will negate need)
UU - situational +3 E/M, Q = 1, S = +2 (can live through an attack, early unit, nothing upgrades)
China (+14<->+12)
UA - +6 (stronger GG, but very tightly focused for a UA, useful all game)
UU - situational +4 E/M, Q +2, S +3 (twin attacks = faster promotions, more dead enemies, upgrades to a non-ranged unit)
UB - +4 (always built, pays for itself and other basic buildings)
Denmark (+15<->+11)
UA - +7/+3 (with major water vs. without; mixes with UUs very well)
UU1 (Berseker) +5 (LS replacement that acts like an overpowered Knight, upgrades to UU2)
UU2 (Ski Infantry) +3 (UU1 upgrades to it, better movement on bald hills+ is good, rest is situational)
Mongolia (+13<->+10)
UA - +5 (taking out CSs usually isn't a good plan, but this helps with that)
UU - +5/+2 (RA replacement for Knight; mixes well with UGP; good until Industrial; useless on water maps)
UGP - +3 (great with the UU, keeps up with the fast army, healing)
Japan (+12)
UA - +7 (solid UA which keeps units alive longer)
UU1 (samurai) - +3 (LS replacement, generates more GGs, but requires the UA to be great)
UU2 (zero) - +2 (fighter replacement, but not very useful in most games)
Polynesia (+14<->+3)
UA - +8/+0 (water map, not water map)
UT - +3/+2/+0 (culture game+water map, water map, not water map)
UU - +3 (warrior replacement, CS reduction ability)
Arabia (+16<-> +14)
UA - +7 (double 'ok' bonuses)
UB - +5 (always built, print your own money)
UU - +4/+2 (RA Knight replacement, solid until Industrial, not good on water maps)
Aztec (+14)
UA - +7 (helps always, especially in domination games to get more SPs)
UU - +3 (warrior replacement, special promotion upgrades well)
UB - +4 (lack of lakes is annoying, but bonus growth is solid)
Russia (+12)
UA - +8 (always helps)
UU - +2 (Cavalry replacement, but still beat easily by multiple old units)
UB - +2 (better pre-patch, but can make for some massive land grabs)
India (+13<->+12)
UA - +10 (solid ICS owner)
UU - +2/+1 (better on E/M, pretty boring for Q/S given that it upgrades to a melee unit)
UB - +1 (Mughal what? who cares about castles after flight?)
Germany (+13<->+8)
UA - E/M +7 Q/S +3 (very situational, but on marathon it's got potential)
UU1 (LK) E/M +3, Q/S +2 (1/2 hammers is good, but the upgrade cost is horrible due to the 1/2 hammers)
UU2 (Panzer) +3 (solid unit, even if some people think tanks are useless)
Egypt (+9<->+5)
UA - +4/+1 (there's only so many times you build a wonder for this to be useful in a game)
UU - E/M +2, Q/S +1 (no resource, sure, but upgrades to a melee unit. useless pretty fast)
UB - +3 (happy from a temple is useful, don't lose the city though)
England (+12<->+2)
UA - +6/+0 (water map/not water map)
UU1 (LBs) E/M +3, Q/S +2 (Gets +range, but not the +sight to go with it. upgrades to a melee unit)
UU2 (SoTL) +3/+0 (better than a frigate, but naval units cost too much for upgrades; water/no water)
Rome (+15<->+9)
UA - E/M +9, Q/S +5 (the higher the costs, the better this is. minor issue - require a base of hammers first, all game)
UU1 (Legion) +3 (can make roads, ok, otherwise just another swordsman)
UU2 (Ballista) E/M +3, Q/S +1 (strong as a treb, but then upgrades to one with nothing special upgraded.)
Spain (+13<->+8)
UA - +8/+4 (more NWs on map/be first/super skilldorado/get to work them, less...)
UU1 (tercio) +2 (just upgrade a pike, it'll be better than making one of these then upgrading two turns later)
UU2 (Conq.) +3/+2 (terra/small continents map, not ... map)
Inca (+13<->+10)
UA +7 (good always)
UU +2 (great for upgrades, poor if you can't dodge)
UT +4/+1 (let's the Incans settle areas that others can't, but if no mountain ranges...)
Greece (+14 <->+6)
UA +7/+2 (useful if you go CS heavy/Patronage, not if you don't.)
UU1 (hoplite) E/M +3 Q/S +1 (temporary and doesn't have anything to upgrade)
UU2 (Companion Cav) E/M +4 Q/S +3 (after nerf, not so great, but extra GGs)
America (+12)
UA - +7 (double bonus, sight great, other side means don't need AW with base tradition)
UU1 (Minutemen) +2 (good unit, but requires new build during the renaissance. soon to be outdated unless you purposely dodge rifling)
UU2 (B17) +3 (Solid late game unit; especially now that SBs get promos. One step closer to double attack SBs)
Iroquois (+12<->+9)
UA - +6 (it's ok, but not super)
UU - +3 (solid replacement)
UB - +3/+0 (better than the workshop with lots of forests worse without)
Ottomans (+12<->+6)
UA +6/+0 (water, barbs, better than German UA; no water... naval units cost a LOT to upgrade)
UU1 (Jan) +4 (best unit in the game for upgrades, but have to make them in Renaissance)
UU2 (Siph) +2 (Lancer replacement...)