What are the downsides to reasoning?
That it sometimes leads to undesirable results and insights?
It might help to think how you'd be if you only had the ability to connect premises to conclusions. You couldn't know if those premises are true, for example.
As a pragmatist, I don´t really care if the are true/True/TRUE. I just care for "what works" within that which appears to be the reality of our existence (which may, ultimately, be an illusion itself).
A downside to experience is that your senses might be deceiving.
For all intents and purposes, it is sufficient for me to know that I share this potential deception with my fellow beings, and that relying on it leads to remarkably good results.
On top, if the results aren´t good, we have great tools to analyse the way our senses work and to spot and explain the causes for the collective deception.
A downside to intuition is that your intuition might simply be wrong.
Yes.
Reason does not only lead from sensual experiences to conclusions, it also is a tool to check the reliability of our senses.
It also is a good tool to check the reliability of our intuition. However, intuition seems to be inherently immune towards analysis and trouble-shooting in case of failure.
On another note, since intuition requires experiences and senses, it just
adds another uncertainty factor
on top of the one that comes with relying on our senses.
I guess what I am trying to say:
What I particularly appreciate about reason is its (self-)correcting powers, and its openness to put itself to scrutinity.
As for "intuition", I guess I still don´t even know what it is supposed to be. I´m tending towards the notion that at worst it is used as a euphemism for bias-confirmation, and at best is the results of reason having become second nature (so that the explicit rational steps can be short-cut). Whereas, if it is posited to be some independent obscure faculty of judgement making, I am not very enthusiastic about it since usually I find the results underwhelming.
It seems to me that reason allows for a permanent "I may be wrong - let´s find out if and why.", whereas "intuition" simply turns out to be right or wrong (in that respect it isn´t that different from throwing a coin), and that´s that (unless we start using reason to explore the mechanisms of "intuition" and the potential error-sources that it comes with).
That said, I am glad the way you worded your question implicitly asks for a reasoned response. "What´s your intuition concerning reason?" wouldn´t leave much space for more than, well, mere appeals to personal intuition, after all.
If in doubt, reason is looking for common ground, whereas intuition insists on individual capability.