NiMH in high mode

I've read that in high mode, flashlights could lose up to 40% output with the NiMH rechargebles. Will you get longer runtime on high or stay the same? Does it depend on the flashlight?

As far as I've been made aware, that mainly depends on whether the light is regulated or direct drive.

They are regulated lights, Fenix LD20 R5 and 4sevens AA2 R5. I'm researching but the information is a little overwhelming at the moment. I bought the Fenix for my father and the 4sevens for myself so I could compare the two. 4sevens site says their light has a buck boost that the Fenix does not. Would this affect the high outputs with NiMH?

I guess the better question would have been: Will NiMH rechargebles affect the high outputs of the Fenix LD20 R5 or the 4sevens AA2 R5?

A NiMh should out perform Alkalines at the higher levels. New Alks vs charged NiMh should have the same output at high & turbo on these regulated lights, but the Alks will drop off significantly faster. Lithium primaries (L91s) should outperform both. Interestingly there are testimonials of Alks outperforming all chemistries at very low draw levels like moonlight.

Both have boost circuits to drive the higher output modes, but only the Quark has a buck circuit to drive the moonlight level. The Fenix should be a little more efficient (better runtimes at the same lumen levels) since it has a narrower voltage range, but it will probably go into direct drive mode on lithium primaries (which are >1.7v new) meaning you might lose a few modes for a while, and the Fenix will not be able to run a 1xLi-ion like the Quark.

Regardless of whether the output would differ (which in the case of the Quark I highly doubt—from experience), I think the consensus here is that using alkaline cells in expensive lights is not recommended because of the risks of venting and swelling, potentially ruining the torch.
Li-ion cells, on the other hand, have been claimed to boost the output of certain NiMH oriented 4Sevens lights, but I highly recommend reading very well into that topic before attempting it (for risk of explosion and warranty-voiding damage ).
I wouldn't dare to comment on the LD20's performance on either type of cell, however.

Unless I'm mistaken, isn't the "turbo" mode in the LD20 unregulated? I believe that might give the advantage to alkalines for maybe the first five or ten minutes, but that's all. I'm guessing nothing you'd be able notice by eye, except in side-by-side comparison.