My understanding, from reading around on the web, is that a stick welder needs a constant current DC, whereas MIG needs constant voltage. Regardless, looking at the schematic diagram of vintage DC stick welders, they don't have capacitors in the output, only a big choke. For those of us not really up to speed on electrical stuff, a choke is nothing more than a wire wound around an iron core. AC voltage oscillates 60 times per second from negative 170 volts to positive 170 volts. The full rectifier makes it so that it oscillates from zero volts up to 170 volts, but now 120 times per second. This is already called DC (direct current). However, it is not filtered. In the power supplies of audio hi-fi devices there is a lot of effort put into making the filtered DC be as close as possible to a constant voltage, like 12V for instance. The role of the choke in the stick welder is to be a buffer for current during the peak of the wave, and release it in the valley thus making sure the current is above zero amps.
@FUTZ if you are wondering how much better it is a "bought" DC welder than mine, it's probably a good deal better if you're talking about a quality unit like a Lincoln AC/DC. That is because they have a purpose built DC choke which will NOT saturate at full current. This is why I cut the core on the transformer I am using as choke, to make a gap. The gap in the core decreases the maximum inductance of the choke, but it allows it to have some inductance when big currents are passing through. Un-gapped cores will work well for smaller currents, but will saturate and have almost zero inductance (useless) for big current.
I have tested my welder last night with 1/8" 7018 rods with the welder dial on 165 amps. It worked very nicely. My understanding is that the 7018 rod works very badly when used on an AC welder. To me, this is the real test. The welds are smooth, and the 7018 electrode melts nicely and evenly.
I know nothing about welding aluminum, but from looking at some TIG machines, they always say that AC is needed if you want to TIG aluminum.