Impossible to say.

I don't know what your backstroke or freestyle look like. You may just be kicking more on your back. You may have a poor head position. Don't know.

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Swimming Workout of the Day:

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2020 National Masters Champion - M50-54 - 50m Butterfly

Try just kicking on your back; i like doing it with my arms stretched out over my head in the streamline position, but you can also do with your arms by your sides. Do say a 50 back kick, then a 50 free kick w/ or w/o k-board, and see how your legs feel after each. This will be more of an "apples to apples" comparison.
As Jason said, you may just be kicking more when swimming backstroke vs swimming freestyle.

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"Anyone can be who they want to be IF they have the HUNGER and the DRIVE."

To move through the water on backstroke, you have to kick. A lot. Freestyle, you can just sort of let your legs do whatever they want. I'd suspect that just the fact that you're actually kicking is the feeling you are getting.

I find kicking on my back in streamline so much easier than kicking in a freestyle position. I'm not sure why that is -- are the muscles used different?

I do sometimes get a nasty foot cramp doing it that I don't get kicking in freestyle position.

I think that the easier feel is due to the fact that we can stretch our feet/ankles better on our backs, but by the same token, this extra stretching leads to the more frequent cramping. I don't get them in my foot but rather in my calf/Achilles tendon, but same thing basically. I wouldn't say that i find backstroke kicking that much easier per se but i do enjoy it more b/c i don't have to use the k-board. I do about 80-90% of my kicking on my back in the streamlined position, and it is espec fun on a sunny day in the outdoor pool. Today I did 9 x 200 m back kick, 4 w/ fins and 5 w/o, as part of my main set, and i've been kicking around 1800 m/2000 yd in almost every workout for last 4 yrs or so. My kicking has improved considerably, and of course my full stroke swimming also, espec in the stroke events, e.g. non-freestyle.

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"Anyone can be who they want to be IF they have the HUNGER and the DRIVE."

No, it's not an indication of weak hip flexors. I "feel" my quads and hip flexors working (a) when I am doing backstroke (b) when I am swimming very fast freestyle (c) when I have done a very long workout

I'm not positive, but I think that backstroke is a more kick-dependent stroke than freestyle. I know that I have a very shoulder-driven freestyle and I think when I backstroke, I get less out of the pull and more out of the legs. Perhaps there's someone around here who has a good back and free and can comment.

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maybe she's born with it, maybe it's chlorine
If you're injured and need some sympathy, PM me and I'm very happy to write back.
disclaimer: PhD not MD

Matt I'm not a swim guru or former collegiate stud just an old dude who loves swimming so take this with a grain of salt. Hands down backstroke has become my favorite stroke the past couple of years. It went from an active recovery swim down to loving backstroke sets to doing ~ 4-500 yards of it in my warm up routine. I will offer this up in support of what was said about streamlined kicking on the back. That is what showed me how to kick with less leg and more hip/core....as in not a bicycle kick. Something else that really helped me was to kick up AND down that is another aspect that made backstroke start to work for me. I swim 'bottom up' as in my kick is what makes it all groove and when I lock an arm in on the catch all I do is focus on recovering the other side hard, boom done, repeat. Dunno if any of that will help you, but since I felt some much of what you did learning back figured itmight be worth a post. Have fun!