Which one of these companies does at better job with free/libre software? I've always had a soft spot for AMD because it's the underdog, but I want to make sure that they are free, too.
They're about the same. Both contribute to linux. Intel's GPU drivers are more complete and open, but their GPUs are not in the same league as AMDs. AMD has open and closed source versions of their driver and are moving more towards the open version (which is already very good). Both companies have closed-source initial boot and AMT-like tech with potential backdoors built into their CPUs.
AMD has been doing a lot of hardwork to get their stuff into mainline (AMDGPU as a recent example) and they opensource a lot of their GPU stuff on github.
On the CPU side, AMD has patched Linux way before Ryzen was available in shops and has been contributing various patches afterwards.
I'd say they are working to get a decent track record for their Ryzen and Vega lineups.
Intel provides a lot of patches for Linux Kernel, for their hardware, performance counters, and their graphics drivers are open source under mainline. I'm not mentioning their wired Ethernet and other various drivers.
Being one of the top contributors in Linux/OSS/FLOSS doesn't allow them to come clean from their 28-core, inadvertently but conveniently miscommunicated demo.
Intel's iGPUs had the best Linux drivers for the longest time, while AMD just managed to mainline their GPU drivers into the 4.15 kernel.
I think AMD is "worse" at it but for understandable reasons. They're a smaller company, so it takes a bit longer for AMD to release low-level manuals. (Ex: still waiting on those Zen architecture instruction timings AMD!!). Even then, AMD releases "draft" manuals which allow the OSS world to move. So the important stuff is still out there, even as AMD is a bit slow on the documentation front.
Basically, Intel is a bigger company and handles the details a bit better than AMD. But both are highly supportive of OSS in great degrees.