Hey there edokat. I haven't tried Depends myself so I can't help you there but I have tried the Abena X-plus you mentioned. They are pretty good diapers in my opinion, though they are only the second brand I have ever tried. They are one of the thickest brands out there and definitely hold a lot before they leak. Also when used with one of abena's boosters they are almost impossible for me to leak. The one gripe I have about them is that they don't have re-fastenable tabs.
As for the Ordering in secret I do have a solution for you! I live at home with my parents and of course keep my DL life a secret. When I ordered my first pack of diapers online I got lucky and it arrived at my door while no one was home. The second time I had the store ship the diapers to a UPS store and I went and picked them up and kept them in my car trunk until no one was home and brought them into my room. I suggest ordering from XP medical, thats where I got my last supply from and if you follow a link from this website a portion of the order goes to DailyDiapers!