The instrumentation will be completely different. The 2020 SDT report covers in detail the science objectives and types of instrumentation needed to meet those objectives. In short, the instrumentation will be focused on in situ microscopic observations and sample collection and caching for possible return to Earth. Curiosity on the other hand is focusing on laboratory experiments on powdered samples, i.e. mass spectrometer and X-Ray diffraction experiments.
What the instruments are exactly will be determined by the selection in process on the 58 proposals received in response to the Announcement of Opportunity, where the latter goes into great detail on what was requested of the proposers.
Update:
The Mars 2020 instruments were selected in July 2014:

The selected instruments are:
Mastcam-Z, an advanced camera system with panoramic and stereoscopic
imaging capability with the ability to zoom. The instrument also will
determine mineralogy of the Martian surface and assist with rover
operations. The principal investigator is James Bell, Arizona State
University in Tempe.
SuperCam, an instrument that can provide imaging, chemical
composition analysis, and mineralogy. The instrument will also be
able to detect the presence of organic compounds in rocks and
regolith from a distance. The principal investigator is Roger Wiens,
Los Alamos National Laboratory, Los Alamos, New Mexico. This
instrument also has a significant contribution from the Centre
National d’Etudes Spatiales,Institut de Recherche en Astrophysique et
Plane’tologie (CNES/IRAP) France.
Planetary Instrument for X-ray Lithochemistry (PIXL), an X-ray
fluorescence spectrometer that will also contain an imager with high
resolution to determine the fine scale elemental composition of
Martian surface materials. PIXL will provide capabilities that permit
more detailed detection and analysis of chemical elements than ever
before. The principal investigator is Abigail Allwood, NASA's Jet
Propulsion Laboratory (JPL) in Pasadena, California.
Scanning Habitable Environments with Raman & Luminescence for
Organics and Chemicals (SHERLOC), a spectrometer that will provide
fine-scale imaging and uses an ultraviolet (UV) laser to determine
fine-scale mineralogy and detect organic compounds. SHERLOC will be
the first UV Raman spectrometer to fly to the surface of Mars and
will provide complementary measurements with other instruments in the
payload. The principal investigator is Luther Beegle, JPL.
The Mars Oxygen ISRU Experiment (MOXIE), an exploration technology
investigation that will produce oxygen from Martian atmospheric
carbon dioxide. The principal investigator is Michael Hecht,
Massachusetts Institute of Technology, Cambridge, Massachusetts.
Mars Environmental Dynamics Analyzer (MEDA), a set of sensors that
will provide measurements of temperature, wind speed and direction,
pressure, relative humidity and dust size and shape. The principal
investigator is Jose’ Antonio Rodriguez-Manfredi, Centro de
Astrobiologia, Instituto Nacional de Tecnica Aeroespacial, Spain.
The Radar Imager for Mars' Subsurface Experiment (RIMFAX), a
ground-penetrating radar that will provide centimeter-scale
resolution of the geologic structure of the subsurface. The principal
investigator is Svein-Erik Hamran, the Norwegian Defence Research
Establishment (FFI), Norway.