My group and I did exactly this! I really like End of the World but the system was a bit rigid sometimes and Genesys has been perfect for us! In fact, we did the Zombie thing in our first campaign.
End of the World is designed to be played in shorter (even one-shot) campaigns. Characters are supposed to die, or go crazy, or give up on the world. Genesys doesn't quite work that way so the first thing I'd consider if you like the feel of the End of the World system is to adjust the critical table. Instead of a 151+ table, reduce it to 100 so every critical has a chance, albeit small, of taking a character out. Suddenly vicious weapons are extremely dangerous, so be careful with this. I suggest keeping all of the results on the current critical table, but simply reducing the ranges.
Also consider reducing the amount of "painkiller" items you give to your players. Painkillers are very effective at keeping a character standing so reducing how much you give makes them a literal lifesaver and extremely valuable.
Where End of the World allows you to add additional positive dice to a pool for a variety of reasons (environmental factors, tools at your disposal, features), Genesys' boost dice can be used largely in the same way.
End of the World has physical, mental, and social traumas (basically critical hits), whereas Genesys only has physical. I love the trauma system in End of the World and I'm considering trying to make a system like that for our second campaign. Maybe a brand new critical chart for when a character drops below strain threshold? There is a lot to figure out here.
Here are some of the stat blocks I used for Zombies:
ZOMBIE STATISTICS: Infected Human [Minion] Brawn 2, Agility 1, Cunning -, Intellect 1, Willpower 2, Presence 1 Soak 2, Wounds 4 Skills Brawl, Resilience Cumbrous Reaction: Infected Human has one Action, but no Maneuvers. Infectious Bite: Infected Human may spend Triumph results during Brawl attacks to inflict the Infectious Bite critical.
Infected Human [Rival] Brawn 3, Agility 1, Cunning -, Intellect 1, Willpower 2, Presence 1 Soak 3, Wounds 13 Skills Brawl 2, Resilience 2, Vigilance 1 Infectious Bite: Infected Human may spend Triumph results during Brawl attacks to inflict the Infectious Bite critical.
Infected Gorilla [Nemesis]
Brawn 4, Agility 3, Cunning -, Intellect 2, Willpower 1, Presence 1
Soak 6, Wounds 20, Strain 12
Skills Athletics 3, Brawl 2, Melee 3, Resilience 3, Vigilance 1
Adversary 2: Upgrade the difficulty of all combat checks by 2.
Nemesis: Roll twice when determining initiative and acts on both rolls.
Vicious 2: Add +20 when determining the result of a critical hit.
We used the following infection rule for when a character was bit. It worked well:
Infection Bite cannot be healed. At the end of each day, check Resilience vs. the severity of Infectious Bite. Failure increases the severity by 1 (advantages and threats should be used narratively). If the severity of Infectious Bite ever equals or exceeds 5, the character dies.
Modify as necessary. If rolling at the end of each day is too frequent for you and your group, roll instead at the end of each week, as is standard for healing from critical wounds. Infectious Bite makes single zombies fairly harmless but means that when they group up they represent a very real threat, because minion groups upgrade their attacks which can result in Triumphs. This makes for some extremely fun moments at the table.
The fear rules also work pretty well.
If you are interested in hearing how this played out for my group, we recorded our campaign for the first season of our podcast, called Melting Plot. You can find it on iTunes, Google Play, Stitcher, or wherever else you get your podcasts.