It depends on the expectations you have. The software capabilities are certainly very rich at OIM of TSL. I only heard that speed and stability is not that good. Bruker is very easy to use, but the data processing is comparatively poor. However, if you can use MTEX (free Matlab toolbox) you have effectively the most powerful tools for data processing and analysis, it is under continuous development and you can directly ask the developer for help and specific tools. Oxfords Aztec is somehow in between. Great detector, quite simple operation, basic post-processing. The weak point is that the post processing is "effectively" still the same as about 5-10 years ago since still Channel5 is used. However, this is also comparable to EDAX TSL.
Bruker offers from the beginning as standard opportunity to save the raw patterns. I can only recommend this to do since it offers many opportunities to evaluate the indexing, phases, orientation solutions etc. I am asking you: Who is not saving the XRD-diffractograms or EDS-spectra and only uses the numbers derived from the raw data? This is nowadays not more state of the art only to save the "estimated" phase solutions and determined orientations. You can have a look at the linked presentation, e.g. what you can still do with the standard EBSD patterns after your EBSD mapping.
Finally, there is no straight answer. You have always to make compromises, but after some years I am still very satisfied with the combination Bruker aquisition and MTEX. If you don't want use MTEX , and you believe "black-box"-software, CrystAlign (Bruker) is not powerful enough to make you happy. If you are experienced enough and you understand all settings and parameters, use OIM of TSL. But you have to make compromises as well regarding the detectors sensitivity and software stability. Use Oxford, if you are a standard user and you don't want very specific data analysis. The detector is very good, and the software offers the basic tools, but not much more. Obviously, for many people this is OK.