Sony Xperia Z1 or Samsung Galaxy S4 ?

So I posted yesterday about the fact I'd be getting a replacement for my LG G2 and after much arguing with my carrier about the poor customer service I've received from them over the last 3 weeks regarding my issue, I got them to at least give me a month free. That just means I'll have to pay the upfront cost (if any) for the phone I choose. So here comes my dilemma, Xperia Z1 or Galaxy S4 ?

Coming from the LG G2, I'm used to having great battery life and impressive performance. While I know the Z1 has the same size battery as my G2, I have a bad track record with Sony handsets and how they seem to suck away at the battery far quicker than other handsets. Then there's the Galaxy S4. While it's technically got an older processor and smaller battery than the Z1, it's still regarded as one of the best Android handsets on the market. It's also arguably the most popular.

So I'm looking for your opinion, in my position which would you choose ? Both are exactly the same price up front and have the same monthly charge.