Abena M4's are the medium size and Abena L4's are the large size. They should be the same thickness. I haven't ever had any L4's, but with other brands I've seen it's usually just a difference in size, not thickness. I've got Molicare smalls and mediums. They're the same thickness. The medium is just much larger, and since it's larger it's got more padding overall, and therefore can absorb more.
The Abena's are a pretty thick diaper already. You can make them even thicker by adding a booster, like the Goodnites Tru-fit pad. I've done that before with an M4, and it was really thick.
Haven't ever tried the Dry 24/7's before. Someone else might be able to speak to a comparison between those and Abena's.
If you plan on using stuffers to make it thicker, just make sure you don't add too many stuffers. Or don't get something that just barley fits you and add stuffers. Make sure the stuffers are below the leak guards. If they're above the leak guards, then it'll all leak out, if you "go".