Personally, I prefer the smaller AXA set for the EE, as I think its smaller, lighter tool blocks are easier to use for the light work for which the EE is suitable.
As to chucks, I found the 6-jaw, the old genuine Buck 6-jaw, to be the most convenient for a wide range of work, particularly for thin-shelled parts.
A good 4-jaw, one of the older best quality steel ones, preferably in the 6" size, (the 8" size is alright, just a bit less convenient to use) is a practical necessity for the EE. Just make up a suitable collection of aluminium or delrin sleeves as needed, to protect the finish on the workpieces.
A good 3-jaw with the two-piece top jaws will pay for itself, as well. Make up a collection of aluminium and delrin soft jaw tops, in which to bore suitable 'nests' for your workpieces.
The most important thing to remember with the EE, tho, is that the high top spindle speed can lead to seriously dangerous conditions when using chucks.
Absent-mindedly twisting the potentiometer knob to speed up the spindle for polishing a workpiece can bring the spindle speed up to a point at which centrifugal force will pull the jaws out enough to release a gently-held workpiece.....at which point, the one of the jaws will 'swat' the workpiece, sending it travelling like a bullet in some unpredictable direction.
Worse, absent-mindedly speeding up the spindle on an EE could, theoretically, bring a 'brand X' chuck up to the speed at which it might come apart rather violently......which reminds me of an old saying 'when the pin is pulled, Mr Grenade is not your friend anymore'.
That 4000 rpm top speed (a seriously hazardous design error, in my opinion, except for special applications....the standard top speed should be 2500 or 3000 at most) *must*....in my personal opinion.....only be used with the 5C collet nose and collets.
One way in which, years ago, we made some decent money on small-parts work with the EE was to consider an adjacent 14" gearhead Monarch as an 'accessory' to the EE.
Roughing out parts 'in a hurry' on the larger lathe, leaving them, say, .005-.010-ish over, and, when time permitted, allowing the parts time to work out their internal stresses before they went into the smaller lathe for the finish work (this was especially important on some aluminium alloys) was often the most practical way to get acceptable quality work done in good time.
(there were some parts which we would rough out, heat gently with a torch, allow to cool overnight, then chill them in carbon-dioxide snow from a fire extinguisher, and allow them to warm back to ambient before final machining.....sometimes the parts had to wait several days before the material would stabilise. few things are a frustrating as to turn/bore/thread a part, have it inspect 'good' when it came out of the machine, then warp or 'crawl' itself out of tolerance in a day or two)
cheers
Carla