I don't have a 360 or XB1... (I do have a PS4 though) so I'm not the best to make a comparison. But I can answer your questions:
does PS4 charge online access?
Yes, unfortunately it does.
Is it more than the Xbox for membership?
It's actually $10 less per year than XBL. (PS+ costs $50 per year while XLB is $60.) Additionally you can sometimes get 1 year PS+ subscription cards cheap from Amazon. So instead of paying $50 you might be able to pick up a year's PS+ for only $40. (US only though.)
I would point out that the PS4's media capabilities have increased a lot since launch with the addition of the Media Player. (Their lan streaming service works pretty good... Plus you can play content off flash drives or external hard drives too. And of course it has netflix and other services like that too.)
Since you mentioned Call of Duty, if you like having first crack at the DLC then you may want to go with a PS4 simply because
Sony secured the rights to all CoD DLC being released first on PS4. (So you know how the 360 got CoD stuff first? Well now it's the PS4 that gets that kind of stuff first.)
One thing I would recommend though is looking into getting the console with a larger hard drive. They normally ship with 500GB hard drives. However 500GB is nothing when games easily take up 30-60GB per game. (Plus each system has a certain amount reserved for itself... Offhand on a brand new XB1 the user has ~360 GB of useable space. On PS4 the user has a slightly more respectable ~400GB.) I don't know if the Xb1 can have it's drive swapped by users or not. But I do know that the PS4 can have it's drive changed without voiding your warranty. Sony even actually details steps on
how to change the PS4's hard drive.