Pretty much. I certainly know it works that way here, indeed we have some 4 different EU nationalities my workplace and all of them just moved in and got themselves a job, no questions asked. Also, in some countries you're even eligible to vote in some elections after residing there for a certain time, citizen or not. Here in Denmark, for instance, after living here for 3 years you have the right to vote in municipal and county elections regardless of citizenry.
Being an EU citizen basically opens up most of the continent as far as working and choosing a place to live is concerned. It's a free reign.
[edit] Which, in my opinion, is one of the best things about the EU. There's so much to see, so much to try, so much to do and so many places to go to, and there are little to no hindrances to doing it other than desire, finances and a little wanderlust. It's a nice feeling knowing that should I feel like it, I can go live and/or work in either of Paris, Berlin, London, Madrid, Athens, Warzaw, Rome, Glasgow, Dublin, Lisbon, Valetta, Brussels or any other interesting EU city with little more paperwork (though rather a lot more moving) required than for moving to a different apartment just down the road. Travel anywhere, live anywhere, work anywhere. That... is cool.
