Whatever they'll do, company policies will only let Safari run on Apple hardware where they want developers create apps to make Apple profit from. Any improvement to Safari is less profit for the Store. However maybe the EU will really force Apple to let other browser engines run on their devices and they'll have to let go a part of the Store. We will see.
On the other side, Chrome runs on any hardware and people using Safari on their iPhone are likely to use Chrome at work or on their PCs. The competition is almost one sided and can't be won by staying inside the closed world of Macs and ìPhones, especially ìPhones because of the internal competition from native apps.