I'm not even sure this is the right forum for this but since I've played with Motion enough to know it will at least do something similar to this (albeit it very basic) I figured I'd post.
Here are two videos.
I'd like to copy the style of certain moments of the videos but have no clue what was used to make them. I understand specific application names may be stretching it a bit but some ideas of software that can pull this off would be great.
Links to youtube usually point to terrible music videos, ghastly copyright violations, and painfully long and pointless experimental pieces. I cannot sit through obscure youtube clips hoping to figure out what you're talking about. Give me exact times and describe the exact thing you're trying to accomplish.
This is my standard sigfile so do not take it personally: "For crying out loud, read the freakin' manual."
I love how it took you more time to slap me around than to open up those videos and take a 10 second look at them. If you don't want to be helpful then please don't respond in the first place.
The videos would be a gross violation of copyright except for the fact they are posted on the bands' official YouTube channels. You may have heard of them....Franz Ferdinand and Modest Mouse. If you think they are terrible I can't help that.
Now that I have taken the time to set THAT record straight....on to the point. You're going to hate this but any part of the videos you watch will reflect the effect I'm inquiring about...the multiple layer effect that looks like it's a moving diorama from 2nd grade. It has 3D dimensional depth but each element (with the exception of actual footage) is 2D as if it was cut out of a piece of paper.
You can do this sort of animation in any application that has a 3D environment, including Motion, AE, Combustion, Cinema 4D or Maya. Each app, however, has its strengths and weaknesses for this type of animation work. Motion and AE are well-suited to a motion graphics process, but are limited to flat objects in 3D space. Motion does not support camera depth-of-field or shadows, so you'd have to manually create those effects. Cinema 4D can create or render just about anything, but the animation process will be a lot more time-consuming and manual.
Regardless of the app you use, this sort of cut-out animation derives most of its production value from the quality of the elements. Taking the time to scan in real paper images and other artifacts can give you more realistic texture and color, which is key to this style. In the end, it comes down to good design and layout skills first, with the particular app you use to do the animation coming in second.