Personally, I do not think that you can compare those two things. My family all got tattoos, but none of us would ever consider a nose job. But I agree with the others and say that it is a personal choice, and our opinion doesn't really matter
My feeling is that it is simply none of my business. People can do as they wish. Nose jobs and tattoos are really no different from any other fashion choice, except that they are permanent and do involve a small risk. People should understand the risks they are taking.
The risks include some actual health risks (infections, problems with the surgery); social risks (they do send social signals and they may not always be the signals you want; they may affect a career if they are visible even when you are dressed for work); and risk of changing your mind later (the obvious one being tattooing a sweetheart's name on yourself and then breaking up with the sweetheart).
People with tattoos think they are attractive. I don't (usually) find them attractive, but they are not trying to be attractive to me. I am slowly become more and more used to seeing tattoos and body piercings, and they don't look as barbaric to me as they used to.