I have some insight here.

There are some advantages and pitfalls in the advisers you have described and I have experience with both.

Researcher in Data Mining: Here most of your research will be focused in the way you can modify the algorithm to attack the task you have at hand, your adviser will want to see some insight from you on how things are actually working and why are you getting the results you are getting. He will be potentially interested in the application, but he has had so much experience with many different applications, that he will want you to use a generic dataset so you can compare it with other works and prove your approach works better.

You will have insightful conversations about your algorithm, and what can you do to modify it, but any insight from the data itself will probably have to come from you.

Researcher in Area X where Data Mining is going to be used: He will probably not care much about the algorithm you use, as long as it is useful in the particular problem he is working with. He will most likely have a problem for you to work with, and he will expect results, good results. You will have good conversations about the nature of the data, and will learn a lot about the field, but you might feel a bit isolated in the Data Mining part.

The main question is, what do you want to do afterwards, if you want to do a PhD, in which kind of conferences do you want to be? Data Mining Conferences, or that area conferences?

If you are going to the industry, having much expertise in a particular area can be both good or bad, depending on he job you are applying to.

As an example, I did my PhD on Machine Learning applied to Molecular Biology, and even though I had all the theoretical framework to apply it to NLP, most places would not look at me unless I had some NLP experience.

I have some insight here.

There are some advantages and pitfalls in the advisers you have described and I have experience with both.

Researcher in Data Mining: Here most of your research will be focused in the way you can modify the algorithm to attack the task you have at hand, your adviser will want to see some insight from you on how things are actually working and why are you getting the results you are getting. He will be potentially interested in the application, but he has had so much experience with many different applications, that he will want you to use a generic dataset so you can compare it with other works and prove your approach works better.

You will have insightful conversations about your algorithm, and what can you do to modify it, but any insight from the data itself will probably have to come from you.

Researcher in Area X where Data Mining is going to be used: He will probably not care much about the algorithm you use, as long as it is useful in the particular problem he is working with. He will most likely have a problem for you to work with, and he will expect results, good results. You will have good conversations about the nature of the data, and will learn a lot about the field, but you might feel a bit isolated in the Data Mining part.

The main question is, what do you want to do afterwards, if you want to do a PhD, in which kind of conferences do you want to be? Data Mining Conferences, or that area conferences?

If you are going to the industry, having much expertise in a particular area can be both good or bad, depending on he job you are applying to.

As an example, I did my PhD on Machine Learning applied to Molecular Biology, and even though I had all the theoretical framework to apply it to Natural Language Processing (NLP), most places would not look at me unless I had some NLP experience.