Right Raman Spectrum of Cyclohexane
First of all, you are extremely lucky in asking this question for cyclohexane: cyclohexane serves as reference material for checking your intensity calibration, so it is one of the few substances for which integrated band intensity ratios are available in the literature.

Integral intensity 2567 - 3068 cm$^{-1}$ is higher than integral intensity 700 - 900 (i.e. 801 cm$^{-1}$ band). At 532 nm excitation, the ratio is roughly 10.3 : 1.


You always have the fundamental $\nu^4$-dependence of Raman scattered intensity. If you look closely, that's $\nu_0 (\nu_0 - \nu_j)^3$ for the band with Raman shift $\nu_j$ for photon count and  $(\nu_0 - \nu_j)^4$ for power. Thus, the relative band area differs depending on excitation wavelength.
For dispersive Raman instruments, the sensitivity is highly wavelength-dependent and this varies from instrument to instrument and for instruments with moving grating also depending on the grating position.  


Thus, for intensity comparisons across different instruments, you'll need to calibrate the intensity axis for the spectrometers (and possibly fold the higher-resolved spectrum with the difference in line shape if that isn't negligible due to integration of broad spectral ranges)
However, when training chemometric models (calibration, quantitation, classification, ...) for one instrument (or maybe very similar instruments: say, same manufacturer &amp; model), as long as that instrument is stable intensity calibration is not necessary as it will automatically become part of the model.
Which is why many Raman spectra are shown as raw (uncalibrated) intensity. 

This doesn't have much to do with "highly sophisticated" Raman spectrometer rather than doing sophisticated calibration or not. And among the highly sophisticated Raman spectrometers, you have tradeoffs that can make such a calibration more or less stable. In fact, different instruments are highly sophisticated in different aspects (e.g. spatial resolution, spectral resolution, signal stability/drift, versatility/possibility to adapt to different experimental setups, ...) some of these influence how easy intensity calibration is and/or how often it needs to be re-done.


Literature:


McCreery: Photometric Standards for Raman Spectroscopy, in: Handbook of Vibrational Spectroscopy, Wiley 2006
McCreery: Raman Spectroscopy for Chemical Analysis, Wiley 2000