even at the risk of being pedantic, it should be referred to as an "X-ray diffraction pattern", not a "spectrum". the term "spectrum" should be reserved for data as function of wave length or energy.
Now for the main question, rather vaguely worded as it is.
There are many possibilities for intensity differences.
- A different diffractometer (type) might have been used. The intensity as function of 2Theta will differ for a Bragg-Brentano geometry versus Debye-Scherrer geometry.
- The source will have to be considered, are the data based on a laboratory or synchrotron source, in the lab how old is the tube.
- Is the radiation monochromatized, it makes a difference if this is done on the primary or on the secondary beam.
- is the radiation filtered , again primary or secondary beam.
- Especially for Bragg-Brentano geometry (the more common laboratory diffractometer type) the sample preparation is super sensitive. Consider packing density, surface curvature, surface roughness, preferred orientation, grain size, grain size distribution, grain shape, grain shape distribution, absorption, sample height, misalignment of a flat sample (surface not exactly parallel to the primary beam at 2Theta = zero)., 2Theta zero errors, primary and secondary slit widths, use of a Soller collimator, size of the X-ray footprint on the flat sample.
- Finally the sample itself, what is your sample source, sample history. The chemical composition, the crystal "quality" etc might differ.