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HOGBOM is the basic CLEAN algorithm. It is very robust, but somewhat slow although this is partially compensated by good parallel programming. CLARK introduces a faster strategy for the search and removal of clean component. However, it may converge more slowly and can even be instable when dirty sidelobes are high, or the phase noise still significant. MX cleans the largest region of the dirty map because the source removal happens in the uv plane. For the same map size, it is slower than CLARK because of the repeated imaging step, but smaller image sizes can be used. It shares some of the CLARK instabilities because it uses the same search strategy, but the removal strategy counteracts this. MX can be very slow for large number of visibilities.
HOGBOM, CLARK and MX may introduce artifacts as parallel stripes in the clean map when dealing with smooth, extended structures. GAUSS, SDI, MRC and MULTI introduce a different (in principle better) handling of those extended sources. SDI is a rough attempt and requires a good prior of the support to work correctly. MRC has unfortunately no notion of Clean Components. GAUSS and MULTI are the most advanced tools, but are slower than the other methods, although the GAUSS implementation is quit efficient.