Romex through attic to exterior panel
Your first quote is correct

NM-B is not rated for wet locations, and Code reflects that in NEC 334.12(B) point 4:


  (B) Types NM and NMS. Types NM and NMS cables shall not
  be used under the following conditions or in the following
  locations:
  
  (4) In wet or damp locations


Furthermore, the inside of any conduit located in a wet location, such as outdoors, is also automatically a wet location, due to condensation issues if nothing else.  This is codified in NEC 300.9:


  300.9 Raceways in Wet Locations Abovegrade. Where raceways are installed in wet locations abovegrade, the interior of
  these raceways shall be considered to be a wet location. Insulated conductors and cables installed in raceways in wet locations
  abovegrade shall comply with 310.10(C).


So, the second bid is trying to low-ball this by doing a not-so-Code-compliant job; I would point this compliance issue out to them and see how they react.  Personally, I would go with neither option; either the cable would be brought up or down inside the wall cavity then enter the panel from the back, or I would have an indoor junction or pull box at where the conduit exits so that a clean transition from NM to THHN-in-conduit could be made.

Another issue...

Going through the top of a NEMA 3R panel requires special fittings, especially if it's being done with multiple conduits.  Normally, a bolt-on type hub fitting is used to bring a conduit out the top of a NEMA 3R panel, but a NEMA 3R loadcenter only provides a place for one hub coming out the top, as this is presumed to be used for a service mast or such.  Further wiring out the top requires the use of threaded (Myers) hubs that clamp the box from both sides and provide a rainproof seal that way, but that adds cost and requires manual knockout punching in the box top.