Which fits better in this context:
Ich hoffe es geht dir gerade/zurzeit besser.
For which degree of formality do they refer here?
It depends on what you want to express in the situation. If someone has an ongoing sickness¹ that is not going to get permanently better (or not for a long time, like cancer), but has its ups and downs, you would wish them
Ich hoffe es geht Dir gerade gut.
and indicate that you hope that they currently have a better period. I would personally not use "zur Zeit", but it means generally the same just over a slightly longer time span (weeks instead of days). I feel that the semantic differences between "gerade" and "zur Zeit" in this context are not widely used, other options include "derzeit" or "heute" or "im Moment".
If someone was sick when you had last contact and you hope that they have become healthier since then you would use
Ich hoffe es geht Dir inzwischen besser.
The difference in formality is marked by the use of "Dir" vs. "Ihnen".
¹ Note that this also applies to external problems such as during war or famine where you know that the overall situation is bad, but you hope that the other isn't suffering at the moment.