  We compare the N=1 F-theory compactification of Donagi, Grassi and Witten
with modular superpotential - and some closely related models - to dual
heterotic models. We read of the F-theory spectrum from the cohomology of the
fourfold and discuss on the heterotic side the gauge bundle moduli sector
(including the spectral surface) and the necessary fivebranes. Then we consider
the N=1 superpotential and show how a heterotic superpotential matching the
F-theory computation is built up by worldsheet instantons. Finally we discuss
how the original modular superpotential should be corrected by an additional
modular correction factor, which on the F-theory side matches nicely with a
`curve counting function' for the del Pezzo surface. On the heterotic side we
derive the same factor demanding correct T-duality transformation properties of
the superpotential.
