Yes, Mootools and jQuery can conflict each other, when you load both on your page.
Ofcourse, they can use same method names, therefore one of both could break.
In my case, I received in Joomla 1.5 errors for removing handlers.

See, I’m a fan of jQuery, that doesn’t say that I dislike MooTools, but when you create a nice Template for Joomla 1.5 and you decide to use jQuery, the hell breaks open when implementing:

<jdoc:include type="head" />

This, is because Joomla 1.5 uses MooTools and Caption javascript frameworks, for the backend admin panel, but also some components may require it.
In this case I would say, fuck it. – I want to have my own choice of which framework I would like to use.
So stick together with jQuery and wrote the following lines in the top of my index.php template:

$headerstuff = $this->getHeadData();
$headerstuff['scripts'] = array();
$this->setHeadData($headerstuff);

Goodbye MooTools and Caption frameworks. – My conflicts are solved!

Javascript frameworks are for easing development and dynamic web apps.
These toolkits enables you to deal with Ajax calls in an easy and fun way and it’s also cross browser safe.

It can be handy, if you know already something about JSON:
JSON (JavaScript Object Notation) is a lightweight data-interchange format. It is easy for humans to read and write and it is easy for machines to parse and generate. It is based on a subset of the JavaScript Programming Language, Standard ECMA-262 3rd Edition – December 1999.
JSON is a text format that is completely language independent but uses conventions that are familiar to programmers of the C-family of languages, including C, C++, C#, Java, JavaScript, Perl, Python, and many others. These properties make JSON an ideal data-interchange language.

It’s a personal choice which of the Javascript Frameworks you should choose.
Basically they are all more or less providing you the same functionality, and they all
contain excellent documentation and API’s with examples.
I will show you the 6 most popular frameworks, and tell you the current version,
download link and which websites these frameworks use. Also the size of the .js file,
which is an important detail.

* = compressed gzipped / uncompressed