I've tried both, every time I try to use cartridge based setup on the 510 based system I wind up taking hits of burnt polyfill within a few hits. Even with modifications it simply can not wick fast enough. This may be because I am using 510 equipment on a 3.7V device. The 510 stuff is a little overdriven like this (it's designed to be run ~3.2V). An atty is good if you want the full flavor and hit strength of direct dripping, past that, I highly suggest just using cartos instead.
Cartomizers solve the wicking problem by having substantially higher wicking surface area. They can have fairly dense wadding to prevent the juice from draining out, while simultaneously wicking the juice to the built in atty very quickly as a a result of the better design.
Considering that a cartomizer is about $1.50, and can be refilled and re-used for anywhere from a couple weeks to a couple months worth of vaping (varies depending on many factors), it's very hard to argue with the value. A 5 pack of cartomizers is about the same price as a single atty. If a carto burns out or starts giving you trouble, you don't have to waste time trying to get it working, just throw it away and grab another one.
With your 510 based systems, you will probably get the best performance from 510 based cartomizers. There are adapters to run KR808 and 901 and 801 style cartos on the 510, but the voltage of the 510 systems may not be enough to really get those to perform right.
Eric