3d game engine suggestions
For the requirements that you have Unity3d is probably one of your best bets. As roy said there aren't any other 3D engines out there that will span that wide a range of platforms. Why do you think that going to a completely code based system would save you from creating a variety of classes with various responsibilities ?
The coding effort and the amount of code and classes will stay the same. The only thing that does change is the way that you interact with the system that you are producing. With any large scale system you will quickly run into hundreds of files. I am just finishing up a smaller sized unity project 3-4 month coding including learning unity it runs at 10k lines of code plus another 8k from external libraries and over 100 classes. But this amount wasn't driven by how unity works it was driven by the requirements of the project. While coding this I have learned a lot about how unity runs and what kind of patterns it requires and will be able to come up with better solutions for the next project. Look back at what you did and think about how you can organize it better. I think it is a save bet to say that you will need about the same amount of code with any other system to achieve a similar result. 
The advantages that unity does have are a good multiplattform support and a excellent asset pipeline. Importing and utilising art assets, 2D, 3D and audio is for me one of the most onerous tasks of this kind of development and it is extremely well supported in unity.
I am developing a 3d shooter game that I would like to run on Computers/Phones/Tablets and would like some help to choose which engine to use.

I would like to write the application once and port it over to Android/iOS/windows/mac with ease.
I would like to make the application streamable over the internet. 
The engine needs some physics(collision detection) as well as 3d rendering capabilities
I would prefer to use a scripting language such as Javascript or Python to Java or C++(although I would be willing to learn these if it is the best option)

-My desire is to use an engine that is Code-based and not GUI-based, an engine that is more like a library which I can import into my Python files(for instance) than an application which forces me to rely on its GUI to import assets and establish relationships between them.



This desire stems from my recent experience with Unity3d and Blender. The way I had designed my code required me to write dozens of disorganized scripts to control various objects. I cannot help but think that if I had written my program in a series of python files that I would be able to do a neater, faster job. 



I'd appreciate any suggestions. The closest thing to what I want is Panda3d, but I had a difficult time working with textures, and I am not convinced that my application can be made easily available to mobile phone/device users. If there is a similar option that you can think about, I'd appreciate the tip.