I agree with Alky that a lot of vets out there really don't know their stuff - are merely guessing a lot of the time. The 2nd opinion is important before very expensive procedures. Your cat had to be right around that magic age where you also have to make the decision if expensive life prolonging surgery is really worth it; I'm glad I don't have to make that call.
Right now, I have a 15 year old dog. In the past year, he's really been slowing down a lot. He has cataracts on his eyes, but sees well enough to get by (he can catch larger objects in his mouth; like the size of about 1/4 of a hamburger with 100% accuracy, but has a little trouble with smaller objects.) We can see that he's at the age where his hips are starting to bother him. He's still mobile, but has a little bit of trouble & hesitates a little bit before going through the dog door. About a month ago, we discovered he has a tumor on his side (I can't remember the type of cancer that it is; but my wife was able to identify it.) We're not going to opt for surgery at his age; and will allow him to live as long as he's comfortable. Then, we'll have him put to sleep. It's a tough decision; part of our culture in the US is to do anything to prolong life, no matter how slightly life is prolonged & no matter what the quality of life is. My wife sees this every day when families insist on aggressive treatment for their 89 year old grandparent who has 0% chance of surviving 3 more months; has cancer that has metastasized to their bones, brain, and other organs, and is suffering. It's part of the reason why we spend (waste) so much money in the US on health care.
Now, if my dog was 5 years old, he'd have been taken to the vet the very afternoon we discovered the growth. Been there, done that (only to have to put another dog down just a few months later.) Been there with cats too - hundreds upon hundreds of dollars in vet bills; transferred to a regional vet facility where we incurred hundreds more just to find out that the cat had no chance of surviving without prolonged suffering. 10 years old... that would have been one hell of a tough decision. Ditto 12 years old for a cat.
edit: incidentally, in regard to that cat, the problem was feline leukemia. Vet #1 couldn't figure the problem out, because vet #1 had vaccinated that cat for feline leukemia when it was young. According to vet #1, "it's impossible to get it after it's been vaccinated." I know now (the vet probably still denies this) that if a cat is exposed prior to the vaccination, then that shot is useless. Our current vet understands this and actually tests before administering the vaccination. (well, except for barn cats - we just get the cheapest care possible for them.)