In my humble opinion it depends on the content.
Though svg was meant to be used on the web, in general raster images are smaller in size/load and render faster than svg-s of an average complexity.

Also the transformations are not supported well in some browsers that you cannot remove easily from your file made with inkscape.

Ok thanks, maybe I'll wait a bit longer.

This is a slightly different thing but >
Say for example you want to have an image that is replaced with another image and some text changes when a button is pressed (without reloading another page such as with php). I've been using a flash swf maker program so far but is there any newer method to do this that is fairly simple?

I learned some svg manual coding but I never really looked at the html5 canvas yet.

There are some ways definitely.
A whole page deals with svg and html next to the manual (which also has a related chapter).

From what I understand, either it will be a long time, or I've even heard that never will ALL browsers be able to support All SVG images. As things are now, all browsers can display some SVG images. But the best advice I've heard and read about, is that if you want ALL your visitors to be able to view the image, it should be in a raster format (PNG, JPG, etc.).

For your 2nd question, you'll want to look into extensions like JessyInk or Sozi or XIA. Find info here: https://inkscape.org/en/learn/animation/ (It seems like there's another one I'm forgetting..... Oh! Tupi is another one (and there still might be another that I can't remember at the moment). JessyInk comes packed with Inkscape, but most of the others will need to be installed "manually". These are all programs which can create different types of presentations. I've had a very little experience with XIA, and I found it fairly easy to understand, well-documented, and easy to use. But I have a feeling most of the others are like that too.

Oops, and Lazur posted while I was typing....sorry for any repetition.

Even youtube uses SVG for their icons... Providing a raster fallback is a courtesy to users of old IE versions, though.

For basic SVG (usage in icons and logos, graphs, or small animations; no flow text, no filters, not overusing masks/clips), browser support is actually excellent, many SVG files (e.g. icons) are a lot smaller than their jpg/png counterparts, and they have a good compression ratio if you serve them via gzip. They can be animated using javascript, CSS or SMIL. The HTML5 canvas is a raster construct.

Take a look at the javascript library demo pages linked from the animation web page Brynn linked. There are many impressive things possible.
Flash is dead (and dangerous) - I've got no flash installed for many years already.

http://caniuse.com/#search=svg
=> (basic = no filter) svg should be fine unless you're living in a country where they still use ie <9 (China)

Does the excellent browser support include raster images within the svg?

Yes, as far as I know, it does.
But you can also just try it out, there are websites that make screenshots for you using different browers, for example browserstack.com and others.