Was Earth's sea-floor always carved with the numerous geological features that we see today, or was it at some point flat and boring as Mars is today?
Yes, in terms of appearances (as in your question), the Earth's ocean basins have more than likely have been carved with features of some kind or another throughout Earth's history; however, the Martian surface is not featureless - not even close.
The reason being that the geological evidence suggests that plate tectonics has been going on for much of the Earth's history, a mechanism that seems not to be present on Mars - many observations and subsequent models show that the plates have been in motion for much of the history of the planet - resulting in trenches and underwater (and above water) volcanoes (subduction ones), ridges (sea floor spreading). Additionally, hot spot activity has given rise to numerous sea mounts, such as the Emperor-Hawaii seamount chain. These features often taken millions of years to fully develop.
Even though oceanic crust is recycled through plate tectonics, it could be assumed that these processes have formed similar ocean-floor-scapes on occasions over a long period of the Earth's history.
One of the main differences is that the processes that form these features on Earth have been, overall, semi-continuous on Earth - whereas on Mars, these processes, if started, died out a considerable time ago.
Was the Earth seafloor always carved with the numerous geological features that we see today?
Absolutely not. The seafloor is where plate tectonics is starts and ends. The seafloor is extremely dynamic and is incredibly young compared the age of the Earth. Most of the seafloor is less than 200 million years old. The very oldest oceanic crust is in the Mediterranean, and that's only about 270 million years old. That's tiny compared to the 4.5 to 4.6 billion years the Earth has been in existence.
Oceanic crust forms at mid-ocean ridges and disappears in subduction zones. This is what makes the oceans so dynamic in geological terms. There are no corresponding processes for continental crust. Continental crust is in general quite old compared to oceanic crust.
Depicted below is a map from NOAA that portrays the age of the oceanic crust. Note how the mid-oceanic ridge plays a dominant role.
The sea floor has not always been carved with the numerous geological features that we see today. In the article "Intermittent plate tectonics?" Science 319.5859 (2008), Paul Silver and Mark Behn show that plate tectonics has come to a temporary standstill at times in the Earth's past. The deep ocean trenches that separate two continental plates on a collision course with one another disappear when those plates do collide. When this happened globally (e.g., the formation of a single supercontinent), the dominant slab-pull mechanism faltered, and that in turn shut down the mechanisms that form the mid-oceanic ridges. The mid-oceanic ridges slowly collapsed under their own weight. The end result was an ocean floor devoid of features.
This apparently happened with the formation of Pangea. The collapse of the mid-oceanic ridges resulted in a vastly reduced sea level. Sea level at the end of the Permian / start of the Triassic was 300 to 400 meters below the present day sea level.
Ocean floor features
The features of the ocean floor include
The abyssal plain.
The vast majority of the ocean floor comprises the deep, flat, and featureless abyssal plain. The abyssal plain is one of the two features of the ocean floor that has been present since shortly after the continents and oceans first formed.
The other ever-present feature of the ocean floor is the continental margins. Continental crust is considerably less dense and considerably thicker than is the oceanic crust that underlies most of the ocean floor. This difference in density and thickness is why the Earth has continents. The transition from oceanic crust to continental crust is rather sharp; the continental slope marks the boundary between the two. The continental shelf is submerged continental crust between the continent and the continental rise. Oftentimes runoff debris from the continent gets deposited at the base of the continental slope; this is the continental rise. The continental shelf, continental slope, and continental rise are collectively called the continental margin.
Subduction zones occur at convergent boundaries between an oceanic plate collides and another plate. The common characteristic of subduction zones is a deep oceanic trench. The deepest parts of the oceans are at subduction zones. Subduction zones are oftentimes associated with island arcs, typically volcanic.
The mid-oceanic ridge.
Long hidden from humankind, this is by far the longest mountain chain in the world. The mid-oceanic ridge is the deep red areas in the above map. This is where new oceanic crust is created.
"Hotspot" volcanos and other oddities.
The Hawaiian islands, the Ninety-East Ridge, and other oddities well removed from plate boundaries -- what explains these? A hypothesis was raised in 1963, that these were caused by "mantle plumes". This was widely accepted for a while, but is losing favor. Whether mantle plumes exist remains one of the most hotly contested topics in geology today.
Per Silver and Behn, and many subsequent authors, subduction zones and the mid-oceanic ridges are not ever-present features. What motivated Silver and Behn was that prior to India's collision into Asia, there used to be a sizable subduction zone between the Indian and Eurasian plates. That subduction zone has been replaced by the Himalaya. No new subduction zone has appeared in the last 50 million years to take place of that lost subduction zone. Supercontinents assemble by subduction followed by continental collision. It stood to reason to Silver and Behn (and many others) that the assembly of a supercontinent would be marked by drastically reduced subduction and mid-ocean spreading. During those periods of reduced plate tectonics, the deep ocean trenches would close and the mid-oceanic ridges would collapse under their own weight.