My first thought watching video #1 is that it looks more like a tech demo than a game. It's a "look at this meaningless but nicely rendered environment for a minute", and gives you nothing else. What is the game about? Who are the characters? Why is that lady being arrested? Why is this island thingie floating? Why is there a windmill on a floating island? What kind of gameplay should be expected?
Next thought was that there are missing details - missing cues - that could take a video like that much farther. Like the sound from the blimp would feel more real if there was a visual attached to it - a camera shake or something to show that the character is reacting to it, maybe some lights or something coming from the blimp to identify it as the source of the sound - if there was no audio, you'd never know anything was happening. That sound just exists in it's own world and doesn't interact with any other part of the video.
Also, as an audio guy, your background guitar, cool as it is, is clipping by the end of the video - the distortion is audible.
The second video does a lot of things better - no more clipping audio, there's gameplay being shown off, but it's a bit generic looking (another portal-inspired first person puzzle game!) and leaves me still with a lot of questions. I see that there ARE mechanics, but I don't quite get what's happening at first glance. All of the character and story potential that the first video had is now absent.
In terms of story vs. gameplay as the subject of a trailer video, a lot of times the target to hit is somewhere inbetween the two videos you've got. But, that depends on the goals of the game, the goals of the video, etc.
Another thought is one about questions-
You want the viewer to ask questions, but you want them to be pointed, specific questions. For example, a good question to leave a viewer with might be "what's going to happen next?" or "I wonder what led up to that blimp approaching" - you want the viewer to want to probe deeper. But you don't want the viewer to ask "why is this happening?" or "I don't quite get what the video is trying to tell me". It's a weird balance where you want the main message of the video to be very clear, but to also have an element of mystery at the same time.
If the point of the video is to show off level design, I think the first one does a better job of that. The first video spends its time presenting a space, attempting to tell a small story with it, and showing of the flashy bits of the scene. It shows off a world-building skill, which is valuable. The second video, while a bit better as a game trailer, doesn't do you any real favors in terms of showing off level design skills. There's a lot more to level design than just the visual parts - and that video doesn't show any of it. A level design video could do something like show a whole playthrough of a level so the viewer could see all the elements that went into it. Why certain elements are where they are, how the level hints at solutions to puzzles, how you can subtly direct a player in the right direction, how the set dressing can tell a story, show off some scripted events, show how you can do things like reward players for exploration, or discourage exploration if that's the goal, etc etc. Show how the layouts, visuals, story, game mechanics, etc. all tie together under an umbrella of "level design".
