You don't need to use SVG if you don't want to. The fonts will never look the same across all browsers because each uses a different engine. However, you can always reset to make it look as close as possible. Here is a quick reset that you can add at the top of your css file that will solve this issue.
h1,h2,h3,h4,h5,h6 {
font-size: 100%;
font-weight: normal
}
Or you could just get a full CSS Reset, like the YUI reset, or Normalize.