Being an EE, I'd say EE :-D But on a more serious note, you'll have to be more specific than just "math intensive". Almost all forms of engineering have a lot of applied math content (sometimes you even need to read some "pure" math!). Apart from Digital Signal Processing and some of Digital Communication/Coding Theory where you will use a fair amount of discrete mathematics, EE mostly deals with continuum mathematics. Things like probability theory, partial differential equations, complex analysis are encountered/used routinely. I can tell you that I am having to read functional analysis and integral equations for my senior project work..so I think it really depends on what you want to do. Mechanical Engineering involves a lot of continuum mathematics depending on which area you're working on...fluid mechanics, solid mechanics, vibrations, automobile engineering. Not to mention Aerospace Engineering which has a LOT of math too! Computer Science and Engineering involves a fair amount of discrete math -- combinatorics, probability theory, number theory, etc. OP from Chemical and Civil should shed some light about the math content in their respective disciplines.
I'm not the OP from that thread, nor am I a ChemE or CivE, however, at my university they both need to take one or two fluid mechanics courses (I believe tensors are involved, but even if not, it's brutal enough, from what I hear--and these were people that were in my first year optional if-the-workload-isn't-enough analysis course). All engineers also have to take numerical methods courses, though the difficulty and workload seem to vary a great deal between discipline, but more so between individual professors teaching different sections. I believe that at the end of an engineering degree, you should have enough math (or math disguised as engineering) to qualify for a minor in math, but you get an engineering degree, so it'd be redundant!
For Civil besides the standard math requirements, you'll see more advanced math in Grad School depending on your PhD field. If it's transportation, you'll see more optimization (nonlinear), and stochastic process classes.
As far as I know, all engineering disciplines use advanced mathematics intensively, especially when one is involved in developing analytical methods and the computational engines for complex analyses. It all depends on how intensive and challenging one wants to be. Taking something like control theory, I've seen the same complex math applied in EE, AeroE and Nuc E. Same theory, but applied to different systems. The state of the art now is computational physics or multiphysics, numerical simulations.
Multiphysics implies multiple aspects of physical behavior, e.g., heat transfer (conduction, convection, radiation) and fluid mechanics (fluid flow), which couples different differential equations. The Navier-Stokes set of equations is an example of multiphysics, in which one simultaneously solves continuity (conservation of mass), momentum and energy equations. The complexity increases when there is a phase change, so one must consider liquid and vapor/gas phases. Further complexity may involve the evolution of chemical species and reactions, radiation and nuclear reactions, interactions of charges with E- and B-fields, fluid-structure interactions (with turbulence and flow induced vibration), and so on. Problems readily become non-linear in spatial and temporal domains, especially when reaction rates or dimensional scales span multiple orders of magnitude.