When you write "AMD and Intel", most likely you're talking about name brands of CPU's. For CPU's there is no other, so there "cheaper part with higher specs" from other brands.
And, of course, brands have many models, with a different price and different specs and different quality. And it's hardly ever true that all models of a certain brand are inferior for their price. So it's not "brand or specs", it's model. And for that, see if you can find reviews before you buy something. You'll find that most reviews are about specs.
If I'm looking at parts for my computer should I go with cheaper parts with higher specs or should I stick more towards name brands such as Intel and AMD? I'm basically asking if I should be worried about brand, specs, or both?