There is a big difference, in my opinion.
When you inline the JS at the bottom of the <body> tag, you're forcing the page to load those <script>s synchronously (must happen now) and sequentially (in a row), so you're slowing down the page a bit, as you must wait for those HTTP calls to finish and the JS engine to interpret your scripts. If you're putting lots of JS stacked up together at the bottom of the page, you could be wasting the user's time with network queueing (in older browsers only 2 connections per host at a time), as the scripts may depend on each other, so they must be downloaded in order.
If you want your DOM to be ready faster (usually what most wait on to do any event handling and animation), you must reduce the size of the scripts you need to as little as possible as well as parallelize them.
For instance, YUI3 has a small dependency resolution and downloading script that you must load sequentially in the page (see YUI3's seed.js). After that, you go through the page and gather the dependencies and make 1 asynchronous and pipelined call to their CDN (or your own servers) to get a big ball of JS. After the JS ball is returned, your scripts execute the callbacks you've supplied. Here's the general pattern:
<script src="seed.js"></script>
<script>
YUI().use('module', function(Y) {
// done when the ball returns and is interpretted
});
</script>
I'm not a particularly big fan of putting your scripts into 1 big ball (because if 1 dependency changes, you must download and interpret the whole thing over again!), but I am a fan of pipe-lining (combining scripts) and the event-based model.
When you do allow for asynchronous, event-based loading, you get better performance, but perhaps not perceived performance (though this can be counteracted).
For instance, parts of the page may not load for a second or two, and hence look different (if you're using JS to affect the page style, which I don't advise) or not be ready for user interaction until you (or those hosting your site) return your scripts.
Additionally, you must do some work to ensure your <script>s have the right dependencies to be able to execute properly. For instance, if you don't have jQuery or Prototype, you can't successfully call:
<script>
$(function () {
/* do something */
});
</script>
or
<script>
document.observe('dom:loaded', function {
/* do something */
});
</script>
as the interpretter will say something like "Variable $ undefined". This can happen even if you've added both <script>s to the DOM at the same time, as I'd bet jQuery or Prototype are bigger than you're application's JS (so the request for the data takes longer). Either way, without some type of limiting, you're leaving this up to chance.
So, the choice is really up to you. If you can properly segment your dependencies - i.e. put the stuff you need up front and lazily load the other stuff later, it'll result in faster overall time until you hit the DOM being ready.
However, if you use a monolithic library like jQuery or the user expects to be able to see something involving JS animation or style right away, inlining might be better for you.