The closest thing to bear a "next gen" GPS label is the new block IIIA satellites, sometimes (officially) referred to as GPS III.
For civilian users, the most notable change in block III is that there will be a signal L2C available on the L2 frequency. With 2 frequencies, you can calculate ionospheric delay, resulting in better accuracy and resilience. Before this, L2 only carried the encrypted military Y code (but L2 could still be used for carrier phase tracking, so industrial non-military GNSS receivers could still make some use of it).
There will also eventually be an improved (backward-compatible) signal on the L1 frequency, and even a 3rd signal on L5. There fundamental system remains the same though, this is more of an evolution than a revolution. E.g, L2C is already available on some block II satellites. For military uses, there are some other interesting changes in block III, notably a new military signal M with a spot-beam antenna that can target a limited area, which is pretty cool.
Russia's GLONASS satellites evolve similarly, with the new 3rd gen K satellites getting more frequencies etc, and using CDMA just like GPS (previously the GLONASS signals used FDMA, i.e. each visible satellite used a different frequency slot). Galileo and BeiDou are also quite similar, but BeiDou is notable for using geostationary and inclined geostationary satellites in addition to regular medium earth orbit satellites (essentially to get improved coverage in Asia). A possibly interesting feature of Galileo is that there may be a "commercial service" signal, i.e. that non-navigational data may be broadcast via the Galileo satellites.