Upgrading only makes sense if you're smart about it, and your current frameset shares certain standards with nicer bikes like (for road bikes) a short brake reach, 700c wheel size and so on.

I wouldn't consider upgrading a bike that doesn't have a derailleur hanger; it's a pretty good indicator of a sort of minimum standard I have - entry-level race quality. Plus, derailleur claws are the devil's work.

If you have a source of cheap parts like a local co-op, piecemeal upgrading can make a lot of sense. Hyperglide is a must... light rims in well-built wheels is usually quite an improvement, along with light tyres... proper front brake... stiff 31.8mm bars... brifters instead of DT shifters... lightweight seat and post, these are all improvements you'll notice.

Without a source of cheap parts, you're usually best off buying another bike second hand, swapping all the best bits onto one bike and flipping the other.