I was with an outfit once that had a bizjet hit a deer that ran across the runway just as it was landing. When they dismantled the nose gear, which was the point of direct impact, they found deer hair inside that had entered through the grease fittings. There will be plenty of goose DNA in the engines when they find them. Not even the fish and crabs will clean all of it out if fuel and oil residues don't scare them away.
Engines running at high RPM when the bird/s entered will produce distinct damage patterns, which are easily verified by comparing them to the damage done to test engines during bird strike certification.
If the engines were dead (still freewheeling) or not producing much power, they would be at low RPM and water would cause a different sort of damage. The black box will reveal a lot about engine state and RPM up to impact.
Water is not as hard as concrete at landing speeds and not nearly as hard as a goose at nearly 200 knots. It will produce a different sort of damage, but this debate will all be moot soon since the odds of not finding DNA if they hit a goose are lower than the odds of the 155 people surviving this would be.