If your concern is about security then nothing is 100% secure not even government sites or any high end sites
denial of service attacks are common in any systems
internet is places for hackers crackers crawers worms trozen horses
but if you want to use Debian Ubuntu its more secure like users said its not known to many unlike Windows and viruses don't sell that much for Mac and Ubuntu as it does for Windows since they can make profit from them in those system.
If are open to use any system without any problems if you know what you are doing and and don't install or click the links that you are not sure.
But Debian Ubuntu is great since you get almost any software for free and from usability perspective its Window like interface for novice users and power shell scripts for veteran who want to try different things.So it really matters what you want to do.But most popup are blocked by defult from Firefox and OS defult setting that comes with Ubuntu.Give it a shot you will know the different you can always remove it easily by doing remove programs if you don't like it.But I prefer Ubuntu since its lot faster and has all I want and don't run any crap background process that are heavyweight and kill lot of processor time.
Hope that helps.