The question is not which frame is prettier. It is what you want the frame to do.
A frame really only has two jobs: holding the piece together, and deciding how firmly it is separated from the wall. Oak and black solve the second job in completely different ways.
Oak: the frame steps back
Light oak has roughly the same lightness as a white or off-white wall. The edge between frame and wall therefore goes soft, and the eye reads the piece as part of the wall rather than as an object on it.
It is the right choice when the room already has wood in it - oak floors, birch furniture, pine panelling - or when you want the terrain itself to be the only thing drawing the eye. Oak also works best when several pieces hang together, because the pale frame does not create a grid of dark lines between them.
Black: the frame sets an edge
The black frame does the opposite. Against a pale wall it becomes a clear boundary, and inside it something more happens: the backing plate behind the relief is dark, so frame and backing merge into a single dark field. The pale terrain then appears to float in it.
On the Åre piece the effect is especially clear, because lake Åresjön is cut all the way through to the plate. The lake therefore reads as dark, and inside the black frame you register the water immediately.
Choose black when the wall is pale and you want the piece to take up space, when the room already has black details such as lamps or window frames, or when the piece hangs alone and has to hold a large surface.
Two cases where the choice is easy
A dark wall. On a dark green, grey or black wall a black frame disappears entirely. Then oak is what makes the piece visible at all.
A pine-panelled wall. Here it is the reverse. Wood against wood with only a few shades between them goes muddy, and then the black frame is what gives the piece its own outline. More on that in the article on decorating a mountain cabin.
With or without the nameplate
A second choice that affects the same thing. With the nameplate there is a small cut-out field carrying the name and height of the place, which makes the piece immediately legible to anyone walking into the room.
Without it, the whole square is terrain. That is a quieter expression and it reads more as abstract form than as a map. Anyone who knows the place will still see it, and that is often exactly the point.
Note that the two versions are separate models, not the same piece with the lettering removed. Without the nameplate, the terrain gets back the area that would otherwise have been cut away.
If you cannot decide
Oak is the more forgiving choice. It works in more rooms, survives a move to a different wall and clashes with fewer things. Black is the stronger choice when you know where the piece will hang and the wall is pale.
See both versions side by side under mountain pieces, or read the guide to choosing size first.