I did not find a explicit comparison with a dish, but this quote does contrast the design with "other possible forms"
The communications
antenna
at Andover
is a much enlarged
version
of similar antennas
widely used on Bell System microwave
relay routes.
A horn reflector of this type with a 20 X 20 foot aperture
was used at
Holmdel in the Echo experiments.
Fig. 12 shows a model of the Andover
antenna.*
For structural
reasons, the horn at Andover
is conical rather
than pyramidal,
as was the case in the smaller versions.
The antenna
rotates
in azimuth
on two concentric
rails and in elevation
about the
axis of the conical feed horn on two large bearings.
Two equipment
rooms are carried on the structure.
The maser is in the upper room near
the apex of the horn.
This configuration
has several advantages
over other possible forms.
It is very broadband,
presents
an excellent
impedance
to the transmitter,
and the parabolic
surface is efficiently
illuminated.
Most important, however, for the present application, the antenna has very
low side and back lobes and may be connected to the receiver with
short, low-loss connections resulting in a low system noise temperature.
(emphasis mine)
Source: The Telstar Satellite System, included in NASA SP-32 Volume I
Lots of detail on the antenna are available in the first two papers in Volume II including better pictures and schematics
- The Mechanical Design of the Horn-Reflector Antenna and Radome
- The Electrical Characteristics of the Conical Horn-Reflector Antenna