Seemly :
I am not worried much about gaming (I will give 1080p a try even if it won't work out well) but I am worried about video editing, I am an animator that uses c4d and that program is pretty demanding. I would say the same for premiere
There are TWO things being discussed here then:
1. Interface:
That is what 4K vs 1080p means. You have more pixels so can afford to decrease the font size relative to the same at 1080p so basically a bit more on screen or simply sharper.
2. Processing:
a) CPU
This is larger related to the choice of CPU. You probably want at least a 4th gen Intel which is dual-core with Hyperthreading and also has a reasonably high CPU frequency. You can Google the Intel site by typing the model name of the CPU and "intel" such as:
http/ark.intel.com/products/76616/Intel-Core-i7-4600U-Processor-4M-Cache-up-to-3_30-GHz
This CPU has TWO cores but can get up to 30% more processing (if program supports) with hyperthreading. It Turbos up to 3.3GHz.
*You can compare CPU's this way for laptops. For example, if you see almost the same model but it only goes to 2.4GHz then that's going to be a lot slower for video editing.
b) GPU:
Not much to say here. You'll probably want an NVidia 700/900 series but this is not my area of expertise. Again, for the most part you need to compare CPU's. There's an advantage to using a GPU (depending on the program, or what the program is doing at the moment) but even in programs like Adobe Premiere there can be a quickly diminishing advantage between GPU performance (such as a Titan desktop vs a GTX750Ti. Huge price difference may be a really small performance.
Quadro workstation GPU's are expensive and not really a part of this discussion.
Summary:
So 4K is more about the INTERFACE being better, and processing ability is more about the CPU (and secondarily the GPU).
Update:
It would be interesting to see what resolution is supported at 60Hz via the HDMI (or DP if present) to a desktop monitor. Most laptops with HDMI support up to 1920x1200 AFAIK. Some newer models have "HDMI v2" which supports 4K at 60Hz if the GPU also supports it (whatever the laptop specs say for output if you can find it).