I haven't used the most recent Bandit 6 but a friend that has one and told me that it has says more bar pressure that the Core. Both are excellent kites, The XR3 and Bandit are different kites, the Core is a hybrid Delta where the Bandit is a C delta, some sort of an hybrid of the C kites. Core<s equivalent would be the GTS2. Core has a universal bar which can be used on all Core kite' sizes, so if you have 3 kites you might want to buy 2 bars only.
If you buy the F-One B7 the safety will be improved were as on the B6 and prior you still have to deal with the velcro system. Most will say that it is not a problem how ever F-One felt the need to update it to today's standard. Having said that, Core has a twist system that is not a standard of the industry how ever, it works perfectly what ever the circumstances. The Core might have a small advantage in its re-launch ability, it is also a bit bigger, 5 struts vs 3 for the F-one.
2 great kites like I have said, if you can try that the best way to feel which one is for you.