Hi ferret6
The Passmark scores (which we 'generally' go by) show a slightly different final result. Passmark for the GTX 970 is 8648 and Radeon R9 290/390 at 6710. So that's nearly 2000 difference which is quite significant.
I see the difference between 290 and 390 is the extra 4GB for the 390, so the Passmark results could be expected to be same between models.
Without reading the whole article, the Overclocking charts indicate that the R9 (Sapphire) is slightly better, or each is very close (as in their Summary). But correct me if wrong, that's overclocked, whereas all the others are not stated with any OC tag, so is the comparison fair?
It's hard to know which is a better choice.

Lumion is not targeted to NVIDIA hardware. The developers attempt to code things to standards, in the past AMD cards did a few things differently and the performance (at least for Lumion) was noted as less by a bit than "comparable" NVIDIA cards. It seems that the majority of our users, at least from Benchmark submissions, are opting for NVIDIA cards.
Key thing goes back to what the client expects to use Lumion for in terms of scene requirements; refer
LUMION 5: Minimum hardware requirements. 8GB will be useful for more complex scenes, but the 'better' performance of the GTX 970 means render times will be better, so the client will save (some) time (and ultimately cost).
Bit of a balancing act between those and affordability. Sorry can't be more clear cut.

Some advice that is current whilst the developers work on things, is that if the scenes are likely to require more than 4GB of VRAM, we do recommend purchasing Windows 7 64bit Pro (which has free upgrade to Windows 10 for a time through to next year). This allows GPU data to be handed off to the system RAM when needed.
Whatever card is chosen, please also make sure a suitable PSU is used.
Attached is the Benchmark results submitted from our commercial users.
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DISCLAIMER: Please note that the above does not mean that I or Act-3D endorse specific products. We are unable to offer any guarantees regarding the expected performance in Lumion with the above-mentioned hardware, and you cannot hold us liable for any costs or damages incurred if you purchase hardware based on our posts on this forum or via email.