I would give advantage to England if they manage to reach the finals. We shouldn't forget that they are playing Finals at Lords. In case of Australia vs New Zealand, advantage goes to Australia and if its India vs New Zealand then Kiwis might win the Championship.
Obviously England will be having an advantage if they reach the finals. With Joe Root in such fine form, and Anderson/Broad destroying the opposition, it will be a very tough task for the other teams to defeat them. However, I would disagree with you on Australia vs New Zealand. Australia lost home series against India recently. Their bowlers (perhaps with the exception of Hazlewood) are not in good form, and the batsmen are also not doing well (with exception of Labuschagne). On the other hand, the New Zealand bowlers are probably the best in test cricket right now, with Kane Williamson and the other batsmen in good form. And when it comes to India vs New Zealand, it is very difficult to make predictions.
New Zealand might be in good form but they didn't play much test cricket in away condition and last time they went to play against Australia in Australia. They faced a whitewashed, they have a problem of getting choked when playing against Aussie. That's a only reason i gave advantage to Aussie.