Should You Upgrade a Prebuilt PC or build a PC from scratch for Gaming?

Depends on which game or games to be played, what is required in hardware and software to play well, and what you can tolerate as to lesser performance, higher budget, the time and effort to make your own custom machine.

With no specifics from you, cannot guess a good answer for you.

I usually pay more when building from scratch, as I use better components than the pre-built manufacturers. Now I can just upgrade individual parts as needed, at my leisure

It depends on how well you can put a PC together and what your budget is.

When I build a PC out of new parts, I'm spending more money than I would if I was buying off-shelf.

If I had more of a limit, I would buy an off-shelf PC with the processor that I want then upgrade the RAM, Video, and Hard Drive as I can.

if its a namebrand pc most components are going to be largely proprietary in most cases, in other words, theyre not going to mix well with a highend component you just try to plug in .. building a box, researching the kikas components that will compliment each other, will be the way to go ..