We can't know. You are losing yourself in vague descriptions without providing any exact and solid technical info like system info, render settings, your source files, version of AE, how you view the output and whatnot. From decode errors during playback to genuine render issues this could be anything, but as it stands, nobody can make any sense of your non-info.
Standard 4K workflow:
- Decide what size 4K and frame rate you want to deliver and set your composition accordingly. If you intend to deliver h.264 then make sure that you are picking a LEGAL and supported frame size and frame rates compatible with your playback device.(check the chart: H.264/MPEG-4 AVC - Wikipedia
- Create your composition making sure that you follow design guidelines and follow recommendations for avoiding things like Judder: FAQ: Why does horizontal motion stutter (judder) in my movies, such as during pans? (here again - you must understand frame rates and their effect on motion, motion blur and their relationship to playback devices)
- Render a DI if you intend to do further processing of the shot, edit the shot in a NLE with other footage, or wish to archive the shot using a lossless or nearly loss format (10 bit is recommended if you intend to do further color correction)
- Render your project for delivery using the Adobe Media Encoder. Note: if you render from Premiere Pro you are using the Adobe Media Encoder. Make sure you understand the limitations of the playback device if you intend to modify one of the presets.
If you simply drag a composition of any size into a composition of another size the nested composition will have to be scaled to fit the new frame size. If you resize a composition, which I think you indicated in your post when you said, "When i try to resize the main comp to H.264 it looks completely different, and it appears zoomed in." the contents of the layers are not automatically scaled to fit the new frame size so the behavior is normal and expected.
You also made no mention of your render settings or your workflow. You only stated that you brought your 4K footage into After Effects and started a new 4K composition. That's not much to go on. What kind of 4K footage? What did you do to that footage? How did you try and render the footage. There are Bugs in Apples Quicktime h.264 container so you should not use that format. Uncompressed, the default rendering option in the AE Output Module, especially at 4K, will never playback smoothly. You have to give us details if the Standard 4K workflow described above does not give you a successful render.