I've always found it to be more expensive to build. It's kind of
sad... because I love the DIY thing... but the reality is that a bike
manufacturer will always get components for cheaper than you can (I'm
not talking about used parts here). Even closeout prices are often not
at the big manufacturer's (or even some small ones) price point.

That being said... I took a year or so to gather parts for a Gios frame
that I got reallly cheap. By the time I was done, I think that I was
riding a full Campy Veloce bike for under $800. The frame was used,
but the rest of it was brand new. And, I got to do it all the way I
liked it....

If you're patient enough to grow the bike over a year or so, you may
save some money. But my advice to someone who wants to build-up is
DONT do it to save money... DO do it because you love the process.