Those of us would relate level design to environment design and visual composition saying “are they not the same?”, when in fact they are not. Well they could be and you can take into account certain compositions of the environment and keep it consistent within the level if you know how to make this effective when designing the level anyway. My answer is they do relate, but level design is much more technical and requires more thought than just visual juiciness. You need to be able to play it and explore it and interact with it and if you had high expectations after seeing just the compositional stills, it all comes down to how well the level was designed resulting in if it will satisfy those expectations or not.
So if I had an order in which to do these relating tasks to make the previous paragraph sound less difficult. I think with the ideas and stories and documentation thrown around, yes, create some concepts and some smashing compositions with points of interest and so on until some finals are ultimately agreed on. I can imagine when given the all clear from the bosses, that is where the level design comes in. The art team must start begin blocking out simple level structures. I know some companies do this to get a feel of space, scales and potential elements of interactivity and scene manipulation (such as walls breaking or buildings blowing up and sinking to reveal more of the environment, as a small example). I can actually imagine the process of level design will require all the different teams, animators, programmers and artists to work together to achieve the right effect for the level.
The process of level design figures out how you will traverse your environment, how you will see important assets, shows you how dynamic and alive it is, tells you how it relates to the game as a whole and so on. Once the initial structure is up, it will be open to constant change in order to deliver the right feel or show those fantastic money shots in the form of cut scenes or camera fixes.
Off the more general views on the subject, it really depends on what kind of game it will be in the first place to determine how the level will be structured. Fighting games like the new Street Fighter 4 series onwards and Blazblue have 3D backdrops that some could consider as level design but isn’t really. Yes you can have dynamic elements and crazy animations but as you shift left to right it is only a visual delight that requires less “level design”. Compare with a first person shooter and you have a lot more work ahead of you. Whatever playable area you have, there needs to be more minute details and elements of interaction from computers that blow up because you just shot them to a crate you need to kick to the other side of the room to get into that vent that is too high for you. ALL 1st person games give you freedom to look about your surroundings making more of a job to grab a player’s attention. That could be in the form of sounds in a certain direction, points which take away your freedom like cut scenes while in your players view or ones that take you out of the players view and while you are playing, areas that narrow down to a linear path so you cannot avoid the an event ahead of you or you need to find a smart way of traversing without getting killed.
Finally, 3rd person games can give you that freedom camera movement (I mean the right analog sticks on xbox and ps3 and the mouse camera movement on pc games) or they can make the whole level or certain parts of that level integrate fixed camera views meaning artists can really work on a sexy visual composition for the level as you are traversing it which I personally think is the most exciting way to design a level to keep somebody hooked while appreciating the artist’s effort to make an area look amazing from different angles. Prince of Persia sands of time was a game that actually allowed free camera movement through the levels but with the press of a button (and a cool whooshing sound), you could play areas in one fixed camera view as to see different angles and perhaps discover ways to get through a puzzly bit. Niiice.