How much higher bandwidth, percentage wise, can one expect from integrated DRAM vs socketed DRAM? 10%?

Intel's Arrow Lake platform launched in fall 2024 is the first to support CUDIMMs (clock redriver on each memory module) and as a result is the first desktop CPU to officially support 6400MT/s without overclocking (albeit only reaching that speed for single-rank modules with only one module per channel). Apple's M1 Pro and M1 Max processors launched in fall 2021 used 6400MT/s LPDDR5.

Intel's Lunar Lake low-power laptop processors launched in fall 2024 use on-package LPDDR5x running at 8533MT/s, as do Apple's M4 Pro and M4 Max.

So at the moment, soldered DRAM offers 33% more bandwidth for the same bus width, and is the only way to get more than a 128-bit bus width in anything smaller than a desktop workstation.

Smartphones are already moving beyond 9600MT/s for their RAM, in part because they typically only use a 64-bit bus with. GPUs are at 30000MT/s with GDDR7 memory.