That's about as close as you can come to 'balancing' a 1/short rest ability against an n/long rest ability. Simply because 1/short rest is strictly superior to 1/long rest.
If balance is what you're hunting for, you might consider starting with a 2/short rest ability, and thinking through what n would need to be on the n/long rest alternative of the same ability.
Day length, of course, is key. If there is any float in the ratio of short rests to long rests, one will be better than the other.
5e is designed on the assumption of 2-3 short rests / long rest, which means a 2/short rest ability would be usable an average of 7 times a day (always either 6 or 8, of course), but no more than 2 uses in a given encounter. A 2/day version of the ability would be strictly inferior. A 7/day ability could be used as many times per day, so would be strictly superior. Anything in between would have greater nova capability and easier management, but fewer uses/day. That's some room to work with in trying to find a balance. Personally, I think it would make sense to assure the n/day ability can be used /less often/ over the day, even on a 2-short-rest day, so'd set 5/day as the upper limit.
Balancing short and long-rest recharges when the length of the day might be more variable is even more fraught. Shorter days quickly favor n/day. At 1 short rest per day, 2/short rest is usable 4/day, so strictly superior to 2/day, strictly inferior at 3/day, even arguably balancing only with 3/day. But, if there's no short rest, it's balanced only with 2/day, and if there are two, it balances between with something in the range of 3-5/day.
Really, the best way to balance short-rest with long-rest recharge abilities is not to.
Just don't give a choice between the two.