I chose my MA school because I was so excited at the opportunity to not be a TA or a tutor but an ADJUNCT LECTURER, to design and teach my own course. I wanted first to make sure that teaching college kids is what I really wanted to spend the rest of my life doing--check, I do. But I also thought that line under "Teaching Experience" of my CV/resume would look great when it came to PhD applications--set me apart even (goes to show how little I knew, since I'm learning via these forums that many MA students get to teach). My MA school was not bad, but it also was not in the top 20 or even 50. And it was unfunded (ouch). I thought the teaching opportunity was just too great to pass up. And the Director of Freshman Composition, also a professor of mine, wrote me a LoR, using my glowing observation report to comment on my ability to teach. Perhaps at 22 I was ill-equipped to know what would be best for PhD applications 3 years down the road, but I was 100% certain that the teaching experience would help get me in SOMEWHERE.
That's all what I thought then.
Now I would say this (repeating a little what others have already said): If the PhD programs you are looking into place heavy emphasis on their students teaching their own courses, then I would strongly consider attending an MA program where you get that teaching experience. When weighing your application against another of equal standing, they might notice you have teaching experience and the other does not and think, "Not only is she an excellent fit in her research goals, but we know she can fulfill the GA-/TA-/fellow-ship offer with flying colors." If the program doesn't require its students to teach at all or not even every semester/year, then the tutoring at a "better" MA school is a more than fine safe bet. Tutoring is a kind of instruction after all. If a program will require you to be a TA to a professor first and then later teach your own course, they might view the tutoring experience as the first step before TAing.
Best of luck!