Strictly from a noise standpoint alone it can be said that an ODFM  receiver is more 
sensitive

The noise as received by a wide band receiver is much more as a narrow band receiver
If we make it even narrow enough we can even detect signals below the natural  noise
This is how Radio Astronomy works, we detect far away space probes or how some
radio amateurs (hams) communicate on very high or extremely  low frequency bands with
very small power and digital modulation techniques.

Extremely narrow band receivers can be made by replacing  the conventional filters
with digital signal processing .
So filtering in software!

In a ODFM receiver we filter often the hundreds of carriers each with such
a digital signal processor
Think it as hundreds of small band receivers on each carrier in parallel..
In reality we have one small band receiver what scans (samples) each carrier
with it's modulation very fast

Maybe this very simplistic explanation helps..


Bob Tenty 
VE3TOK
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