It depends on a few things really.
Like for me my old rig died, I moved to console and just found it easier. I had a laptop for doing odd bits instead, I found this meant I didn't need a big old desk and all the peripherals. So you unlock space for other things and also save money on the elecy bills too lol. In short, I scrapped a big desk, a thirsty machine and add ons, traded it for a big old sofa and a better TV for a PS4 Pro (at the time) and had the option to wander about with my laptop should I want to. Gaming laptops are great if you buy right, maybe repaste it, undervolt it and possibly make a custom cooling tray. Bigger high pressure fans shift more air quieter than the small fans going noisy nuts inside the laptop otherwise. High power parts and smaller form factor will always give you heating issues, making it a noisier option at times too, but you should buy a laptop knowing that.
As for the eGPU, the more I looked into it the more it looked a false economy because decent cradles cost a bomb, The razer one is like 350 on it's own, then you have the 400+ of the GPU itself and even then, the interface and attached bus speeds can give you a sub par performance anyway. Personally I'd say budget for your laptop, then what you'd have to spend on the eGPU stuff, and spend that amount on the best laptop you can afford. Repaste, undervolt and a decent tray. you have full portability less noise than could be.
For example when my girl aint well, I can sit next to her while she's watching stuff, so I can keep tabs on her. Other times I can link it up to the TV and use a USB controller, I can also move anywhere in the house comfortably, even took it away to a cabin with me so we could watch netflix in the woods.
Summary.
Obv, PC gives you best power and performance, interchangeable parts for upgrades and all that, but you need a lot of decent peripherals to make the most of that power, all adding to that cost outside of the actual machine itself. You end up needing a lot of space for that too and you can't move it about freely.
Laptop allows you to have portability at the cost of some power depending on the machine itself, most you would need is a decent mouse and a headset. I would say cooling tray but that's personal choice. You have the option of a eGPU but I'd say you're better investing that extra cash into a better laptop and an a custom cooler really. Downside is, you're stuck with what you bought, for me that's not an issue cause I don't need the bleeding edge of tech every 3 months and I don't mind stuff not being 4K ultra on everything either.
