Ok I am going to keep this somewhat brief...
Advantages of Linux:
1. Security-
In the past, and even some in the present, the default security policy on windows was to have the default user be the administrator. This opens up TONS of security holes, and is part of the reason Windows is considered so insecure. The other major OSes out there have all shifted away from this to my knowledge(DISCLAIMER: Lack of knowledge on Solaris etc.) and have both a superuser (root in linux's case) and a regular user that is used day to day. This basic change makes a huge difference. Vista I believe moved to this as well, to an extent, but unfortunately I have seen more than a few factory installed systems that do not follow this, and when people do follow this in Vista, Vista has about the most annoying approach to this.
2. Openness-
Open source, means just that. You have complete access to everything about it. It also means that 5 years down the road, if a project dies, changes licenses, or whatever, you can easily fork off the last version that was open and continue it. It means that in most cases, if a piece of software is used commonly, it won't die easily, but if it does, you can continue it yourself should you choose. It is more than just being free price-wise, and while it may not mean much to you now, wait until you get on an IRC channcel, report a bug, and have the developers troubleshoot it with you, and fix it then and there(This has happened for me several times).
It also means that in most cases, your OS won't be loaded down with DRM mechanisms only there to make your life miserable and make you purchase music, videos, etc. multiple times. On the flip side, this also means that on occasion with new technologies, it isn't immediately supported(HD-DVD and Blu-Ray with AACS were not until cracked ie.) In general this is not to much of a problem however IMO, as they tend tog et supported in an open method sooner or later, and I prefer not having to worry about DRM crap.
3. Stability-
This goes a lot with security, but in general(There are always exceptions) Linux I find to be more stable than Windows. I spent several years in IT. I know how to stabilize Windows, or did up until Vista rather. Vista I won't touch. In general a decently set up system in Linux vs Windows, the LInux system tends to be more stable. A piece of software may crash, but you are much less likely to have crashes take down the entire system.
4. Customization/Choice-
This is the big one, and the reason why Linux tends to be scary to so many folks right off. There is a LOT of choice to be made with Linux. Distributions make a lot of that choice for you, depending on which distribution you get you will start with many choices made for you in how they see them being made. But that doesn't mean you can't change them.
This also leads a lot of linux newcomers into a problem, as there is so many choices, and so many ways to do things, it can be very confusing at first. I can customize a linux desktop to run on a touchscreen enabled PDA, my audio workstation with very low latency performance, a router, a NAS... the list goes on. This is just what I have done recently in my own home. But in many cases people don't need all that choice, so distributions like Ubuntu, or eLive have come along, with an overall vision for something they see as being useful to people. They make a lot of choices for you, so your first choice comes to which distribution to use. That can be a tough choice sometimes, for many people the standard Ubuntu, eLive, Fedora, or whatever works fine. For others it won't.
There are many more reasons. There are drawbacks as well, in many ways Mac OS is a valid choice for many people. It has a much more user friendly administration, has many of the advantages of above over windows. However it also locks you down to the Mac 'experience' and is very difficult to customize even close to the level I can with Linux. Even changing how my desktop acts or looks is difficult in Mac compared to Linux. But it is stable, and a good experience for many folks that don't want that choice.(DISCLAIMER: This post was typed on my Macbook Pro with Mac OS X. I am going to put eLive on here as soon as I get moeny to order a larger HD and replace it though

On to your specific comments:
Quote:
| 1. Save money on software. Almost all of my software now is open source - having an open source OS would be one step nicer |
If most of your software is already open source, you have likely crossed one of the most troublesome hurdles for many people going to Linux. Your software likely already works, but double check it and know what will and won't work. In many cases Open Source software is cross platform, in many cases it may have even started on Linux, BSD, or whatever. But often times folks have specific closed source programs they think they need, and finding a solution for this can be the first catch. If you do, post them up and you will likely find suggestions for replacements, or how to get them running.
Quote:
| 2. I would like to be able to increase the speed and utility of the notebook. I have heard the Linux is more streamlined and compact so am hoping to achieve some benefit from that. Is Linux appreciably faster than XP? more stable? |
This goes into that customization thing above. Ubuntu Linux, a dsitribution of Linux, for example is a good choice for many people coming to the world of Linux as it is very user friendly. But it is not known for being the fastest distribution around(Though I believe it has improved slightly since earlier version, I haven't tested it lately). On the flip side, Gentoo Linux, a different distribution, is not exactly user friendly, but extremely customizable and very easy to get VERY fast. There are other distributions that form a middle ground however.
In as far as increase in utility, it all depends on what you are planning to utilize the notebook for. What are you planning on doing?
Seablade