The following is anecdotal, but conveys an answer to your question quite well, I think.

I have a long history of being considered overly professional, too strict, and robot/lacking interpersonal skills.  I’ve spent a lot of time working on this as a leader, both prior to and during leadership roles.

One of the key, consistent pieces of advice I have ever received is to be yourself.  There’s no one way to be an officer – neither hard-nosed or overly compassionate.  If you’re not YOU, your troops will notice and you’ll have a tougher time.

So… when to be tough and gruff and when to be caring depends on how you personally would handle a situation.  For me as a PL, I defaulted to an officer who didn’t get involved in NCO or enlisted affairs except on rare occasion.  I never grew close to my troops because of that.  I knew I cared about their well-being, but I cannot, to this day, guarantee that they knew.

As a company commander, I softened up significantly.  I took opportunities in formation and in public to dig in to the groups and individuals under my command to get to know my troops better.  I often spent some time each week interfacing with troops at their level rather than in a formal setting.  I’d address Soldiers who looked happy or concerned or worried or distracted to see why they felt that way.

More importantly, when punishing a Soldier or when a personal or professional issue was brought to my level, I treated them as people rather than Soldiers with rank on their chest.  I showed that, even in situations where I had to administer punishment, I did so recognizing that it had both personal and professional effects, and I tried my best to show I cared about their well-being.  I often would follow up or preface my decision to render a punishment with my reasoning, which centered around unit integrity and discipline, development of the Soldier, and the desire to see them bounce back and grow.

Just remember this lesson that I’ve learned along the way: the image of the gruff, disinterested, stoic officer that we get exposed to in our formative years is NOT the only form of professionalism.  That is, professionalism has many different forms and factors, so be the best you that you can be.