In all honesty and reality, every race has its pros and cons;
different personalities of different people may be more attracted or suited to different races; someone may be all about technology and imperialism while someone else may be all about mass, cheap production or someone else yet may be a mixture of both.
You can read what other people have to say about each race, but if you really want YOUR opinion or if you truly want to know how YOU feel about a race, you'll just simply have to play as that race for awhile, taking on different opponents, difficulties, and map styles.
Personally, I love playing as multiple races (The Japanese, Vikings, Franks, and Byzantines are the four most-frequently played races by me) for variety.
I can tell you right now that my personality does not sit well with the race such as the Mongols, Aztecs, or the Goths. Yours, however, might.
But generally;
Land maps are not well to be played with Vikings because one of their unique units is a long boat, or the Koreans because one of their units is a turtle ship.
Water maps are terrible to be played with any of the Central American Races (Aztec/Mayan) because their dock system is not that great.
If you happen to have the game, which you probably do, then you should be able to look at each race's technology tree;
it gives an extensive overview of all technologies, which ones are available for research in that particular race, and if that race receives these technologies free as they progress through the ages. Plus, it also tells a race's main strength; the Britons are a "Foot-Archer Civilization"
and the Franks are a "Calvary Civilization" and the Vikings are a "Naval Civilization" and the Byzantines are a "Defensive Civilization." Some races have multiple strengths. Plus, if you are on a team, YOUR Civilization gives bonuses to your allies, and of course so do your allies to your Civilization. The Japanese bonus is that all ships have "+15 line of sight" or something rather. Huns allow allies' stables to produce 20% faster. Britons allow allies' archery ranges to run 20% percent faster. Spanish allow allies' trade profit 33% increase. Aztecs allow relic gold production to be increased by 33% for allies.
Whichever you decide to play, a race will always have it's strengths and weaknesses; unless of course you select the "All Techs" option, but that really defeats the purpose of having multiple races; like a big middle finger to the game makers' faces who worked so hard to invent multiple races.
And lastly,
there is no such thing as the "Best Race" or even the "Worst Race"
on Age of Empires, because every race is suitable to different people.