I have the Xperia T and I wish I would have waited for the Z since T is only dual core and not water proof. People tend to like the S4 but I'm not sure what that phone is offering on top of what Android offers, which the Z will have like media apps, such as walkman. And don't forget that PlayStation Mobile is available on Xperia phones, which will let you access Sony's new game and app storefront that is compatible with PS Vita and most likely with the PS4.
http://www.android.gs/samsung-galaxy-s4-vs-sony-xperia-z/
Here is a comparison that has S4 winning in an 8 point battle, winning in Processor, Storage, and OS; while losing in Design and tying in Connectivity, Camera, Display, and Dimensions.
No doubt the S4 has a strong processor, but the storage win is shallow in that the S4 has 16/32/64GB options and the Z only 16GB, but both can take MicroSD cards to expand storage. The S4 does have the 4.2 OS while the Z has 4.1.2 but the Z is upgrading to 4.2 later. The S4 does have the Samsung TouchWiz user interface if you like that kind of thing instead of the straight Android UI set up.
They tied on Connectivity, Camera, and Display. Connectivity is practically the same except the S4 does have Infared, whatever that does. Camera might be tied but the Z does has slightly higher MPixel count and probably better patented software for stabilization and autofocus but I would test them in person. The S4 added some extra camera features that the author says are kind of pointless, so I don't know. Display wise the Z has a slightly larger screen but they both have the same pixel density. The S4 has an AMOLED screen which should be brighter and use less battery but the color might be kind of off.
Xperia Z won in design and it really does look sexy. Best of all it is waterproof. What a perk right?
This comparison does not touch on Battery or on Price. So make sure to take that into account. Both phones run off contract at $650, contract price can vary. Battery wise the Z does 550 hours standby, 11 hours of talk, and 40 hours of music while the S4 hasn't released its battery life it does have a larger battery...but that processor might mean it isn't going to last as long as the Z.
Since I'm absolutely loving my Xperia T, I'd go with the Z as it is just an awesome better version of the T. It all depends on what you find more important and what you like better if you can test them out at a store.
EDIT: added the battery and price part and PSM
Before the PS3 everyone was nice to me :(
