Its hard not to feel guilty - we just have to do the best we can.
Personally, I am in the camp of I'd rather euthanize than watch them suffer IF the foregone conclusion is that their end is near anyway. In other words, rather than do some treatment that is going to be painful/uncomfortable and will maybe give them another few weeks/months, I'd rather put them to sleep.
Years ago the kids wanted a dog, so we adopted Rex, who was about 13 months old. We figured he was past the worst of the puppy stage, but still had a lot of life in him. Thinking we'd get a healthy dog if we got a mixed breed due to "hybrid vigor", we didn't worry about breed but instead focused on qualities like size, hair coat (didn't want a dog that needed to go to the groomers every few weeks) and temperament. We thought we had found all that in Rex, and as part of our adoptive process, we were allowed to take him to our vet for a once over. When we walked in, the vet said "Are you here about his hip dysplasia?" Think blank looks. "No, we're here for a general physical - we just adopted him". He took x-rays and pronounced it one of the worst cases of hip dysplasia he'd ever seen.
We did have the option of returning him to the rescue but....we were already fond of him so instead we told them the prognosis and determined to give him the best life we could until he was in too much pain to enjoy life any more. He was one of the happiest dogs I've ever known. His tail had a little white tip and I loved seeing that little white tip coming waving around the edge of the bed to visit me in the morning.
After 3 years we noticed he got up from a lying position more slowly and couldn't run as fast. After four years, that side of his rump had atrophied to the point there was no muscle left there and he was clearly in pain. We did do a course of anti-inflammatories and pain meds, that bought him another 3 happy months. But last September, when we'd had him 4 years, 4 months, and he was only about 5 1/2 years old, we realized - that little white tip rarely waved any more. He was no longer happy. We had already been carrying him up and down stairs for about a year, and lifting him in and out of the car. He wasn't a candidate for hip replacement surgery (we had considered it), and we decided we wanted to do it while he was still able to walk into the vet's office on his own, rather than be in so much pain we had to carry him in.
It was one of the hardest things I've done - not made easier by the fact that he rallied when we got to the clinic and was so excited to be there, he was actually straining against the leash to pull me in faster. They did a great job, giving him a blanket to lie on on the floor, and a sedative so he would be relaxed. I held his head and felt him go. His head was wet from my tears and I cried from there all the way to our barn where we had decided to bury him. I still look over and think of him every time we ride past his grave, but know he is no longer in pain, and that we gave him the best life we could for the time he was with us.
I do think that sometimes the best gift we can give them is to let them go peacefully.