TITLE: Complex analytic vs algebraic geometry
QUESTION [30 upvotes]: This is more of a philosophical or historical question, and I can be totally wrong in what I am about to write next.
It looks to me, that complex-analytic geometry has lost its relative positions since 50's, especially if we compare it to scheme theory. Are there internal mathematical reasons for why that happened?
As we all know, lot's of techniques which were later adapted by algebraic geometrers were originally developed in the complex analytic setting (sheaves, local algebra machinery, etc.). In the 50's, Serre, Cartan, Grothendieck and others seemed to have been developing scheme theory somewhat in parallel with complex-analytic spaces (results on coherent sheaves, base change and cohomology theorems, etc.). But already in the 60's it seems like complex analytic geometry started to lag behind - Grothendieck developed Hilbert scheme in 61, and it took already 5 years for Douady to build a complex-analytic analogue. Then in the 80's came Fulton's monograph on intersection theory, and as far as I can tell intersection theory monographs in the complex-analytic category are starting to appear only now. Finally, there is a lot of foundational algebraic work on stacks, and it seems that the amount of publications on complex-analytic stacks is far smaller. 
And in general, my impression is that the amount of people doing foundational work in complex analytic geometry is minuscule compared to algebraic geometry (in the recent years I've only come across works of Mauro Porta about the derived complex-analytic set-up and analytic stacks), compared to how active it was before 1990's (there was a nice summary of results by Grauert and Remmert here going back to 1996, showing how active the field was).
Edit: 

As others have pointed out in the comments, I should have been more specific about what I meant by complex-analytic geometry, since areas like Kahler geometry are very active right now. I basically meant that fundamental side of complex analytic geometry, which shared machinery with algebraic geometry in the 50-60's.
The point of asking this question at all is (besides curiosity) to learn whether there are some well-understood limitations to the subject. As I said in the main post, it appears that the number of people in the 50's working on scheme theory was comparable to that working on complex-analytic geometry, and I find the decrease in the number of people in the second cohort rather surprising as we keep getting new powerful techniques which originate from the complex-analytic treatment (like the creation of multiplier ideal sheaves among other things).

REPLY [3 votes]: For what regards Intersection Theory in Analytic Geometry, in my (nonexpert!) view it is important to take a look at the work of D. Barlet on algebraic cycles on analytic spaces. In his paper “Espace analytique r´eduit des cycles analytiques complexes
compacts d’un espace analytique complexe de dimension finie”, pp. 1–158 in Fonctions de plusieurs variables complex, Springer Lecture Notes in Mathematics, He shows as the set of compact $n$-cycles $\mathcal C_n(X)$ of a reduced complex space $X$ carries the structure of complex reduced space. Moreover, He also proves that  this space coincides with its algebro-geometric counterpart, the Chow monoid. In the loc. cit. paper, one of the most interesting thing is the introduction of an Intersection Theory for cycles on a complex reduced space. It turns out (not really easy to prove) that the subset $\Omega\subseteq \mathcal C_n(X)^{\times 2}$ consisting of cycles intersecting properly is "really big" and that the intersection map (where defined) has nice properties. Recently, D. Barlet and J. Magnusson also published (Springer) the first of a two-volume series Complex Analytic Cycles.