It depends on if Google is doing this as a dedicated business case (if they want to make money as an ISP) or specifically to try and accelerate the growth of high-speed connections.
If it's the former, make money as an ISP, then going up against Verizon at this stage wouldn't make sense. They'd want to do that much later; better to cherry pick as much as you can first. This is what Google claims they're doing.
If, however, they're doing this in order to spur the advancement of connectivity (which is what some analysts think they're doing), then Verizon bumping up speeds to a gigabit is a win for Google. They'd be getting exactly what they want. In this scenario, they don't really want you to get a gigabit connection from Google, they just want you to have a gigabit connection (so that they can use it for future high-bandwidth Google applications).
In terms of technology, at this point both Google and Verizon are deploying exactly the same thing, GPON. That gets you, aggregated between however many households you split to, 2.4 gigabits per second downstream, 1.2 gigabits per second upstream. This is shared among all the houses sharing the same optical signal. Verizon started out using BPON at the start of FiOS (622 Mbps down, 155 Mbps up), but then later switched to GPON, which is also what Google is using.
One notable difference is how television is delivered. Google uses IPTV, sending the television service over an IP network, that same internet connection. Verizon uses RFoG, which basically just takes a cable television signal (870 MHz of it in Verizon's case) and shoves that on a separate wavelength. Verizon FiOS television is basically digital cable, although they have some extra stuff they tack on top of that over the data network. The core of it, the TV channels themselves, is just digital cable though.--
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