Which would you rather see in a basement for wiring?
Old BX or new Romex?

My personal preference would be new Romex installed through holes drilled
in the joists (NOT stapled to a beam or the underside of the joists). If
the BX is not stapled in place, you can use the old cable to pull the new
Romex through.

If drilling the joists is not an option, I would use surface mounted PVC
conduit and individual wires.

On the other hand, if the original BX cable is still in good shape, there's
no immediate need to replace it. Just replace it where needed and update
the rest to Romex as time and money allows.

That said, I've heard local codes in some areas require conduit or metallic
shielding for ALL wiring. I think the Chicago area was one of them, but I
don't remember for sure. You might want to check with your local permit
office (and probably get an electrical permit).

I'm certain that the old cloth had a 60C temperature rating if any;
new NM-B has 90C. Does it really make a big difference?

Lower temperature wiring can be a big problem around light fixtures. The
heat from the light makes the insulation brittle, which flakes off and
leaves exposed conductors. I've worked on lots of lights in old houses that
have completely bare wires, just waiting to start a fire. Kind of scary
when you open it up and see that.

Still, you don't necessarily need to replace the entire run. Just mount a
junction box nearby and run the higher temp Romex from the light to the
junction box. Then tie the old cable into that and join the two cables in
the box. Replace the circuit later when you have the time.

Anthony