Currently, I switched from using mutt to neomutt, although I use the
same configuration for both (in the standard mutt location).  When I
install muttprofile, mutt is automatically installed, even if I have
neomutt already present.

It would be nice to allow a dependency on either package so folks can
choose which version they'd like to use and don't need to have an extra
package installed if it's not necessary.

Control: tags -1 + patch

I suspect something like this would provide the change you want.

diff --git a/debian/control b/debian/control
index 14cf454..f16616c 100644
--- a/debian/control
+++ b/debian/control
@@ -10,7 +10,7 @@ Vcs-Git: git://anonscm.debian.org/collab-maint/muttprofile.git

 Package: muttprofile
 Architecture: all
-Depends: ${misc:Depends}, perl (>= 5.8.1-1), mutt
+Depends: ${misc:Depends}, perl (>= 5.8.1-1), mutt | neomutt
 Description: utility to choose profiles in Mutt
  A profile in Mutt is simply a specific subset of the configuration. You may
  have a personal and a work profile, each of which uses the same base