Is detergent tank necessary for pressure washer?
The pressure in both models is controlled by the tip installed on the wand. On the output side of the pump there's a small valve which opens at low pressures creating a siphon which is connected to a detergent hose. When the black tip is installed the detergent is pulled up through the hose into the water stream. The other tips run at higher pressures and don't draw any detergent.

With either machine you can stuff the detergent hose into a pail and siphon straight from the container. That's pretty convenient for exactly the length of the high pressure hose; after that you're moving the machine and the bucket. Onboard detergent tanks allow you to easily drag the whole unit along. (Note how the tankless machine has twice as much hose.)

On the other hand, the onboard tanks are bolted to the machine and have no drain cocks. Unless you're planning on turning the washer upside down or sucking detergent out with a turkey baster any that you don't use is staying in there until next time. That's probably why they provide two separate tanks, so you can two different chemicals on board and just move the hose to switch.

If you need a highly mobile setup the tank is a nice touch. It's also good if you use the pressure washer for small jobs frequently. For example if you use it to knock mud off a tractor or dirt bike every week then having to refill the detergent tank every month or two beats getting out a bucket and the washer both every week. For everything else it's completely extraneous. Most of the time you probably won't even use a detergent.