The cost of supporting an elderly dependent seems comparable to raising a child. I think raising a child probably costs more, but there are many overlaps.
Body wipes - good ones - cost quite a bit. Wet Ones are $3.29 at target. Cheaper fare at Target may run $1.99, but those cloths are relatively dry (cannot get the job done) and are of lower quality (rip more easily). Diapers aren't too expensive, but add up over time. Incontinence of an adult is much more problematic than with a small baby. The amount of urine and feces is much greater and usually a simple diaper will not do. We've had to use women's pads - such as Poise or Maxi(mum) - inserted into a diaper, which is on top of a bed absorbent pad. That is three layers of padding right there and doesn't factor in clothing (and/or sheets) that is soiled that either must be thrown away or laundered quickly. Good bed pads can be costly over time. Medline Ultrasorbs (which hospitals use and can be bought on Amazon) run 25 (pack) for $39.99. Then you have things like condom catheters and urine bags, which usually run something like $1.50/unit and $8/2000 ML, respectively (for known/good brands). Trash bags are a must. You will have LOTS of soiled and dirty stuff to dispose of, but they also are great at serving as a protective layer.
You better have good insurance with a low deductible. Otherwise, medical bills will potentially crush you.
Walkers, rollators, wheelchairs, bedside commodes, raised toilet seats and toilet handles, shower benches, hospital beds, movement sensors, and the like are sort of the equivalent of baby/toddler protection/convenience devices (just for the elderly, instead).
If you go the nursing home/assisted living/memory care unit route, expect $75,000+/year for a good facility. We were warned by many medical staff that lower-rated and cheaper facilities can be horrible. They are understaffed and the staff that exist often don't and can't do a good job. Bed-bound residents can go months without being turned and get wounds so gruesome they come out of a horror movie. I was told by one hospital nurse, the worst case she ever saw was a woman coming from a nursing home where the staff didn't turn her in bed (or, at least, not enough) and she had a bedsore go so out of hand that the entire skin on her lower back was simply black. And in some areas, the tissue had died and rotted so bad that you could flat out see white bone. It was horrific and she said it was the proudest she ever felt nursing that woman back to health. The entire hospital floor staff cheered after many weeks when that woman was able to heal and finally "go home" (hopefully to better care). These $50,000 and below facilities in my area can be hit or miss (mostly miss). $75,000+/year is where the care is very good - adequate staffing, actual RNs (not just "skilled nurses"), good amenities, professional/nice/caring staff, nice facilities, etc.
Senior health aides are another option, but run typically $30/hour with 4-hour minimums. That's $120/day at minimum. That's the equivalent of a babysitter for a child.
Medicare is pretty great overall. I'm shocked how cheap coverage is for equivalent stuff I'd have to pay for as a non-senior. The premiums are cheap, deductibles are low, and coverage is fantastic in most cases.