Well, as seems to be the standard introduction on here, but we're talking about a long period of history in regards to the Abyssinian Empire, lasting from the 1100's (not including the former kingdoms) until 1974. So obviously there will be differences depending on the time period. Part of Ethiopia's "power" has been its geography; mountainous surrounded by desert.

Now the question of power is relative. Abyssinian was always fairly regionally powerful. It was able to defend itself from a few invasion attempts by outsiders on a few occasions. The 1500's was a particularly active period for invasion attempts. The Ottomans were able to conquer some parts of the periphery of the Empire, mostly along the Red Sea (roughly analogous to modern day Eritrea), but didn't conquer the heartland of the empire. One of the most well-known periods of Ethiopian history was the invasion of Ethiopia by the Adal Sultanate, which was located in modern day Somaliland. The Somalis (with the help of some Arabs and Ottomans) were able to invade the Ethiopian Highlands. But this victory was quickly over when the Ethiopians were able to push the Somalis back out of the highlands after the death of the Adal leader. Now it should be noted that many historians (and any Somali) will say that the Ethiopians were only able to expel the Somalis with the help of the Portuguese who had contributed soldiers and weapons to the effort. The Ethiopian-Adal conflict was in the context of Ottoman and Portuguese fight for control over the Red Sea.

Traditionally "Ethiopia" or Abyssinia consisted of the regions of Tigray, Amhara and Shewa. But under the reign of Menelik II (1889-1913), the empire expanded south and east and west to what are basically the borders of modern-day Ethiopia. Menelik II was able to conquer kingdoms, namely certainly Oromo kingdoms, and the Sidama, Wolaita and Gurage kingdoms. Menelik II was able to conquer these kingdoms with relative ease.

In comparing it to European countries, again it would depend on the time period as European powers went through periods of power and decline. The most notable encounter with a European power would have been during the first Italian invasion in 1895-1896. The Italians attempted to invade and conquer Ethiopian and add its to its colonial empire, but the Ethiopians were able to soundly defeat the Italians at the Battle of Adwa. There was a reversal in 1935-1936 when the Italians again invaded Ethiopia and were able to defeat the Ethiopian armies and gain control of Ethiopia. This is in addition to Ethiopian interactions with the Portuguese in the 1500 and 1600's. Now I don't know enough about European history to say whether or not it could rival European powers at anytime; but Ethiopia had strong warrior culture, and that with the Ethiopians' knowledge and familiarity with Ethiopia's geography meant that it had the upper hand to outside forces.