Why do different instrumental filters use different magnitude systems (Vega vs AB)? Suppose I wanted to construct the spectral energy distribution (SED) of an object. Further suppose I observe this object through the 9 broad-band filters using the Subaru Suprimecam (just for an example) here: http://www.naoj.org/Observing/Instruments/SCam/sensitivity.html

As the statement below the table of broad-band filters says, the Johnson-Cousins filters (capital letters) are on the Vega magnitude system whereas the SDSS filters (lowercase letters) are on the AB magnitude system. I understand what these two magnitude systems are and how to convert between them.

My question is: what is the point of the two sets of filters being on different magnitude systems, one Vega and the other AB? It's not as if the Johnson-Cousins filter hardware physically has the Vega spectrum built into it, right...? 

If I do aperture photometry on an I-band image and an i'-band image, will the first one return Vega magnitude of the object and the second return AB magnitude of the object, by default? And if I wanted to do SED fitting, then I need to be consistent such that all of my data points (even from other telescopes) need to be on the same magnitude system (e.g., convert the I-band Vega magnitude into an I-band AB magnitude)? (Or do that conversion first, and only then convert to flux units via $\nu F_{\nu}$ or $\lambda F_{\lambda}$).
I'd guess it's largely a matter of historical accident and inertia, mixed with a certain amount of taste.

Vega magnitudes are the traditional system, based on how bright the star Vega is within the filter (+ detector response, etc.). The Johnson and Cousins filter systems were defined back in the early 1950s when Vega magnitudes were the default, and were to some extent meant to reproduce earlier photographic magnitudes. The AB system was proposed a bit later (1960s) and was originally used for narrow-band photometry and spectrophotometry, not broad-band photometry like the Johnson-Cousins and similar filters. Some more modern filter systems -- such as the SDSS filter system -- have been defined using AB instead, because the creators preferred it.

Some filter systems have both definitions. For example, the near/mid-IR filters of the IRAC camera on the Spitzer Space Telescope have both Vega and AB definitions; some papers use one, some the other. (Sometimes papers that are part of the same overall project.)

If I do aperture photometry on an I-band image and an i'-band image, will the first one return Vega magnitude of the object and the second return AB magnitude of the object, by default?

By default, no. Doing aperture photometry implies choosing a calibration: that is, a conversion between observed counts and magnitudes. (Such a calibration might already be provided in an image header, e.g., from SDSS.) It's certainly possible to do aperture photometry on an I-band image calibrated to i-band, and vice-versa. I have on occasion done things like aperture photometry on R-band images calibrated to K-band, though I certainly wasn't expecting things to be very accurate.

if I wanted to do SED fitting ...

I think the answer depends on what form your model SED is in. If for some reason your SED is in AB magnitudes, then, yes, you'd want to convert all your observed data to AB magnitudes. If, on the other hand, your model is in flux units, then you'd want to convert your data to flux units (either Vega mag to flux units or AB mag to flux units).