First of all the theory and practice of indicator kriging is much simpler than disjunctive kriging. You can use the common geostatistical software for kriging but you must transform the data using indicator transforms. In general with an indicator transform you must choose a "level" (at least for continuous data) or possibly several different levels.

Indicator kriging is usually attributed to Andre Journel (formerly at Stanford) and I think it was intended to be a substitute for disjunctive kriging.

A little history helps to understand.  In the case of a multivariate distribution it is well known that the conditional expectation is the minimum variance estimator. Moreover when the multivariate distribution is Gaussian (not just univariate) it is also easy to show that the conditional expectation is linear and in fact is the same as the Simple kriging estimator (in fact this was some of the motivation behind G Matheron's work)

The first readily available papers on disjunctive kriging appeared in the proceedings of a NATO  ASI in 1976 (the ASI was held in 1975),  "Advanced Geostatistics in the Mining Industry",   Y.C. Kim, H.P. Knudsen and I published a research report about disjunctive kriging. in 1977 for the US Dept of Energy but it was not widely disseminated. It is too long to put on the web and I only have one copy. M.E. Hohn  (Multivariate Petroleum geostatistics) included some of the material from the report.. There are two papers in WRR,

1986, S.Yates, A.Warrick and D.E. Myers, Disjunctive Kriging I: An Overview of Estimation and Conditional Probability Water Resources Research 22, 615-621

1986, S. Yates, A. Warrick and D.E. Myers, Disjunctive Kriging II:Examples Water Resources Research 22, 623-630

There were several (commercial) software packages that came from the Center for Geostatistics (Fontainebleau, France) that included disjunctive kriging. That software was intended for the petroleum industry and hence quite expensive (Do a search for GEOVARIANCES).

The first edition of "Geostatistics" by J.P. Chiles and P Delfiner (J. Wiley) and to a somewhat lesser extent the second edition as well discuss disjunctive kriging.I don't believe there are any open source codes for DK.

If you look at Mathematical Geology (Mathematical Geosciences) you will find some papers on DK and quite a lot more on indicator kriging. DK is based on an assumption of bi-variate Gaussian distribution (a much weaker assumption).

Both DK and IK attempt to generate an estimate of a local probability distribution (as opposed to an estimate of the conditional expectation)..

There is no simple answer to the question of which is better, theoretically DK should be but also much more complicated and you would need to generate your own code (unless you have a very big budget for software). IK is not based on any distributional assumptions.

Disjunctive kriging is using hermite polynomials, and from that point of view is too complicated. DK is sensitive on the stationarity assumption. According to some authors, can be replaced by a robust median IK. Also the estimates are very smooth. ISATIS is the only commercial software that has DK. For your study I see no benefit in using DK vs IK

Thanks for valuable comments. Answers are very useful.