(The SSEES used to be part of KCL!)
Both are fairly unique in the UK - only a couple of unis have War/Peace departments in the UK and a couple have eastern european courses
What attracts me to the UCL course is that I would have the opportunity to explore different areas - economics, politics and even sociology. Additionally not all of this is geared directly at Eastern Europe. But I also find Eastern Europe really interesting and wouldn't mind studing that region. I would also be able to learn a language ab inito (should I wish to).
War Studies is fairly concentrated in that respect (although there are a couple of modules you can choose from)
What put me off at the interview at KCL is that most people were interested in the Ministry of Defence (MoD). Some were already in regiments and the army was paying for their undergraduate course. Others were planning to join after they graduated (not as in infantry but in other areas - e.g. intelligence).
This is from talking to current 2nd years at KCL in the War Department and not the prospective students that were there at the interview stage.
This is not to say that EVERYONE on the course in interested in joining the MoD but a significant number are (or atleast that's the impression I got). This is something that I don't find appealing. Personally, I am not interested in joining the MoD in any form.
I find it quite a tough decision....
Plus I found the UCL campus better
Both KCL and UCL had great atmospheres when I visited