I use both and would take ChromeOS for the full desktop browser over DeX. I hate mobile browsers with a passion. Today, I had to bid on something on Ebay while at lunch and mobile browser in desktop mode let me down again. Only thing is there are usually better spec'd (mid vs low end CPU, 256GB NVMe vs 64GB eMMC, 8GB vs 4GB RAM, etc.) and deals on Windows laptops which can also multi-boot other OS'.
Windows > ChromeOS > DeX