Actually both of these boards are SoCs and can be used a standalone system. As you said, both of them also support OpenCL. The main different is the specifications of the Cyclone FPGA and the ARM core. There are also some differences in peripherals; e.g. DE10-Nano has a HDMI port, while DE1-SoC has VGA, or DE10-Nano has 7-segment but the other one doesn't.
For both of these boards you can run a light-weight Linux on the ARM core and then access the FPGA from that Linux using the direct connection available between the ARM and the FPGA. Furthermore, the external DDR memory is shared between the ARM and the FPGA. The network port is also likely accessible from the Linux. C and OpenCL are supported on both platforms, but I am not sure about Python.