Server 2008 R2 RDS looks very cool, once you've enabled the "Desktop Experience" and enabled themes. This could be overkill for a thin-client scenario, but if you want to make it more friendly, it's quite good.
Stability: I guess only time will tell. 2003 is certainly more more tested solution, but 2008 isn't exactly fresh any more
Security: Out Of Box security is probably fairly good, but this also depends on your thin client, and whether or not it supports all of the latest protocols. Restricting to NLA sessions is a good idea, but only if your clients support it.
Cost: The biggest cost is going to be supporting it. The time taken by you/your team/technical support. This is only something you can really answer yourself. If you're going to have to fork out for 2008 training when you have 2003 support up to scratch, go with 2003 as it will be cheaper in the short run. But if you have to fork out for training anyway, makes sense to go with the much newer solution.
You mention you already have 2003 licenses, and depending on how many you have, this could save quite a few dollars. If you're a Non Profit and you're paying a grand total of $25/user, then things could be different.
Management Tools: IIRC, they're both pretty much the same. Please correct me if I'm wrong.
So, advantages of RDS? Themes for one. Support for bi-directional audio means that you can connect your line-in devices to the TS as well. If you're running Thin Client, things like Web Access and Media Centre redirection won't matter very much. But apart from that, RDS is a lot the same as TS, and TS was pretty similar between 2008 and 2003.