At first glance, Ethiopia's only merit seems to be making a very strong defensive empire that bunkers down and wins via culture (or possibly science/diplomacy). The passive is quite strong, and when combined with certain culture policies and/or wonders can make even a small (and thus, cheap to maintain) army incredibly powerful. Their unique unit furthers this plan, though as with all unique units they are only online for a limited amount of time and especially for a non-militaristic approach their importance is relatively low.
But they have a hidden gem, which comes online on turn 1, the Stele.
Replacing the Monument, this building simply adds an additional 2 faith on top of the normal 2 culture.
To realize how strong this is, it's important to understand what other ways faith can be generated in the Ancient era:
Shrine, a building which gives 1 faith and takes Pottery research to build. It also does nothing else.
The Celts passive which gives 1 or 2 faith per city if they settle and never improve adjacent forest tiles.
Allying with a Religious city-state.
Adopting a Pantheon which gives additional faith for specific terrain/resources/buildings.
The fairly obvious reason that getting faith EARLY is important is that the first Pantheon is cheapest the form, and the first religion will be the easiest to spread because there will be no competition.
IMO, really only two civs have a huge advantage on founding the quickest religion, Ethiopia and the Celts.
The Celts have the POSSIBILITY of a quicker religious start. However, unless they can settle next to THREE un-improved forest tiles, Ethiopia wins out. In an AI game the worst case scenario if you are Ethiopia and the Celts exist is you will form the 2nd pantheon. You will still almost certainly form the first religion.
On top of this, you give up your passive for this benefit, and it restricts those tiles to being near-useless to work. Their unique unit and building are solid, and in no way am I saying the Celts are not good. Some would argue they are, or can be, the best religious civ. The extra happiness from their unique building also supports a more militaristic game (and their unique unit as well but lets be honest at spearman tech level how often do you really want to conquer the world).
Ethiopia however, gives up nothing really for their early religion. You want to build a monument immediately in most games anyways, so it will be up on turn 10. This means at turn 15 you will form your pantheon. You may be able to make it more like turn 8 and 13 if their is a good tile to work in your city.
They don't give up a passive for this benefit, and they don't restrict any tiles around their city (and future cities) or require any special considerations where they settle new cities.
With their passive, you can play a really fun religious game with about 3 or 4 cities. This leads perfectly to a cultural victory as well. You can focus most of your resources towards improving culture, spreading religion around the world, and maintain a relatively small military force that is extremely powerful
You also have a few civs like Byzantine which have religious bonuses once they are formed. The problem with Byzantine though is that nothing helps them get religion going. This means they are going to have to heavily devote their early game to generating faith, possibly by setting in poor terrain like desert or tundra for pantheon benefits, or expanding rapidly to build extra shrines and having huge happiness problems. If they do none of this, its quite possibly they will never even found a religion.
Food for though, as I haven't seen anyone really talk about these guys yet!