I do not seriously believe that leaving the EU will make any difference as far as border security is concerned. We are not in the Schengen area so we have the right to check people's passports as they come into the country.
Are we seriously going to require EU passport holders to apply for visas before trying to come to the UK? No. Are we seriously going to ban EU nationals from coming to the UK? Nope. The worst that will happen is they will get their passport stamped 'Leave to enter the UK for 6 months' - or something like that. That will suit many EU nationals, though not the honest ones wanting to live in the UK.
Terrorists won't give a damn. Once they're in the country they want to be in they can pretty much make themselves invisible and not worry too much about overstaying their welcome.
Would passport checks have really prevented the Paris disaster? No. Either those terrorists would have had genuine 'clean' passports - with no warning signs that would flash up on the computer at border control - or they would have had faked 'clean' passports, which also would not have flagged up any warning signs.
And if by chance they were carrying passports which, unbeknownst to them, did flag up 'danger' at border crossing points, then they would have been stopped by UK immigration - then, now, and in future, whether or not we're in the EU.