Wetters, if you have been using Depends or Rite Aid or similar quality store brand, of course they are not adequate, especially at night. They are the lowest absorbency end of the range and really designed for people who are going to leak a little bit intermittently or are very sedentary and are going to have someone else do the changing/washing of clothes/bedding for them immediately upon soiling. They are not adequate for the active, independent adult with incontinence and perhaps some other physical limitations who needs reliable "social continence" in public or not to deal with his or her own extra laundry, etc. from poor quality products.
I used both brands that you mention when I first started having medical issues-- not expensive, readily available, sounded reasonable until I was flooding everything on a regular basis, even without full incontinence. Brands from medical supply companies like Tranquility and Abena AbriFlex are the highest absorbency end of the range, much different from the cheap stuff, and will hold much more. According to this link from a supplier I have used occasionally, the Depends Silhouettes pull on underwear in medium reportedly hold 16 oz. Contrast this with Tranquility overnights with 34 oz. and Abena Extras 37 oz. More than twice as much, even if the practical capacity isn't quite as much. I think it comes closer than many lesser products.
http://www.northshorecare.com/pullons1.html Some time ago, while I didn't wet in my sleep, medical issues were regularly causing extreme urgency first thing upon awakening, combined with extreme exhaustion whereby I could not get out of bed fast enough. I tried various female urinal devices, which were less than satisfactory. Of course, I didn't like the idea of flooding expensive Abenas with a full overnight bladder first thing in the morning most days, but my point is that they hold up with capacity to spare, though thankfully, for me, that happens much less frequently now.
Of course, if you want to move up to a brief style diaper and deal with tabs or flaps-- I personally know I physically can't on a regular basis-- that's your choice and I wish you well, but if you prefer a pull up style or find them easier to manage physically, there are several better options than what you've been using and it's not necessarily true that you "must" move up to briefs.