"Abstract in an artistic meaning" is still pretty vague, as some of the answers here demonstrate through their divergence. There are two major interpretations of the term 'abstract':
- One is a sequence of art movements and their derivative styles - from post-impressionism to cubism - that is known as abstract art, synonymous to and/or an increasingly prominent characteristic of modern art.
In this sense, abstraction is image-making devoid of any direct or obvious analogy to the (visually) perceivable world.
- The second is the process of abstraction (which is not unique to the visual arts), where abstraction is a representational simplification of what can be perceived (with any of our senses, really). This simplification can be due to technical or artistic reasons. Every work of art is abstracted to some degree, as pure representation is impossible.*
Obviously, the term 'abstraction' can refer to both meanings, and the term for the disposition prevalent in the arts in the first half of the 20th century is directly derived from the meaning of the word in that second, broader sense.
As for your questions:
Would it make sense to state that one of these picture is more abstract, in an artistic meaning, than the other one, and, if so, which one could be deemed more abstract?
Per my delineation I'd say both are abstracted, but, unlike the first, the second one can be regarded as an abstract image, and here is why:
Nº 1, 'Titan', is a stylized version of what can be viewed as a probable scene: on Titan, one of Saturn's moons, floating on a sea of "ammonia-rich liquid water"1, against a rising or setting Saturn, we see several boats with occupants on the horizon.
All components are plausibly connected, on scale, with a uniform and physically plausible colouring scheme, and in uniform lighting. In that sense, this image is realistic. The only abstraction here is the stylization, in this case a diminishing of details (to improve the atmosphere and overall impression).
Nº 2, 'Mars', lacks all of these properties. It is a composition of elements related through association, not through a potential 'mise-en-scene', like poster nº 1. Furthermore, the distinct elements are themselves abstracted to such a level that they become icons - symbols that signify not a specific object, but the concept of a generic object (e.g. the spacecraft consist of but two polygons, the astronaut's profile's a single line).
What would be the best categories to use to distinguish these two styles?
Nº 1 is narrative in character, it's dramatic, romantic, and epic. I'd say the closest you can get to naming the style of this design, is by pointing out the emphasis it places on capturing a cinematic atmosphere; I think it is intended to imitate a film poster. The big title and the catchphrase at the bottom corroborate this.
The artistic style is even harder to place - its abstraction (e.g. the painterly flow of the reflections in the water) seems independent of what it tries to communicate. It's realistic illustration, but difficult to narrow down more.
Nº 2 is as flat as possible, the only depth cue is the overlap in the elements which are configured purely for compositional purposes. I think this poster's style can be considered 'flat design' (see here for a related Q&A).
According to Wikipedia, flat design
"is a style of interface design emphasizing minimalist use of simple elements, typography and flat colors.
[..] It is easier to quickly convey information while still looking visually appealing and approachable."
Where poster Nº 1 is a movie poster, this seems to be more of an ad or an informational poster. It invites the observer to "visit the historic sites" on Mars. Of course, in that sense it is also narrative, suggesting Mars has been colonized for a significant amount of time, so it can even be regarded as a 'fictional prop'.
* The only possible exception I can think of now is photography, but that's for another time and place.