I did notice that the spell checker in my browser is marking "systemize" as incorrect, though Word says it's fine (U.S. English).
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I think "systemize" is uncommon enough to lead you to prefer "systematize" — and "just sounds weird" is often a good enough reason all by itself.
The word "system" is derived from Greek. In declension of some Greek words the word stem is longer than the simplest form; in this case the simplest form is "systema", but the stem is "systemat-". Analogously, thema and schema are declensed "themat-" and "schemat", respectively. In derivations the stem is usually used, e.g. systematic, schematic.
In my ears then, "systemize" sounds as weird as "themize" or "schemize" would. That is, they sound as if something is lacking. But this is probably only the case with those that were tought the classical languages in school.
As far as I can understand, systemize is a neologism born in business environments where such things are common. Business - and to a lesser degree economics in general - is one of the fields where, or perhaps the field par excellence where neologisms are coined more often than expressions already in use are employed. Systemize would sound negative in a philosophical context.
Systematize means both "to build/draw a system from/out of something" and "to apply systematic laws on something under constraints of consistency and final efficiency". I underline the definitions I give are mine and I am no authority of any kind in this matter. A complete definition of systematize would be "to identify the laws OR rules it works by and define them collectively as an organism, to be abstracted and treated as a model of rules of interaction between the given variables, as defined by their hierachy."
Hierarchy of variables is nothing more than an expression I coined myself and I have no clue whether it has ever been previously spoken of and under which definition. I employ the term model as it is employed in economics and game theory. The definition I gave is pretty circular in my own eyes, but when it comes to semantics applied to define logistics I cannot honestly do any better.
Perhaps it may be useful to notice here that, in Italian, sistemizzare [literally to systemize] means "to quickly and cheaply make something safe and well working, weeding out 'noise' or errors", "to clean up a set of notions or actions". Sistemare [literally to system (!)] instead means "to tidy up", "to settle". Sistematizzare, literally to systematize, only means "to make something work like a system, like an organism", implying that the something was not originally supposed to be able to do it and it cannot happen without human work. The only word among these three that refers to something supposed to be a system is sistemare.
I would draw the conclusion that systemize is, in philosophy et caetera, the "parody" (so to say of course!) of systematize, a "should-have-been systematizing". In business and management environments instead, it is used to define the subordination of a shapeless mass of stuff to a set of pre-existing rules, in order to make it comply with an external system it must be blended into. This system may or may not be the one and the same with the set of rules.
As in all derivational languages, prefixes and suffixes are the key divide (term no one could tell me the English translation of, and that I eventually found on an The Economist title page - "The Gay Divide", last October. In Italian we say "il discrimine", literally translated as "the discriminant").
Another hint from Italian adjectives: sistematico means "constantly happening under given conditions", and it is often used to mean the exact opposite - "all else variable, this stubbornly keeps happening" because of the Italian ethos of implying anything and everything, including contradictions. In the earlier case, the system we are referring to is the small world the something is a cell of - in the latter case, it is the big world that spans the barriers of local conditions and imposes its external dominant laws. Sistemico is instead a word only used by physicians. It means that a process is found to be happening throughout the whole body, the whole system, and is not generated by a local phenomenon.
As you see, the semantics behind these terms are all completely different. It must be that system is such an episteme in itself that it works as a root morph, declined to apply to minor "local" epistemes.
English goes by ear. What it sounds like is what it is like. I cannot add anything more.
Thanks for reading.
The NOAD reports systemize is "another term for systematize." That is all the description given by the NOAD; I guess that means systemize is not so often used.
I am not sure how the lexicologists would argue about it but I see systematize as 'making something systematic' and systemize as creating a system from something. They are certainly not the same thing.
The OED defines systematize as:
implying that an existing system is followed in arranging something.
In contrast, the TFD quotes the AHD thus:
Fuchs, et al., (Ed.), Internet and Surveillance p.139
I could be wrong, though.
Just saw this online. Hope this also helps because I also have the same problem.