It’s impossible to say which of you is unreasonable- as a pp said, tone and context are everything in these situations. I honestly suspect, as is the case in quite a lot of disagreements, that you are both somewhat in the wrong. It does sound like the kind of comment that could be said pointedly in a passive aggressive way and probably not the most tactful thing to say on a date night, especially if he already knows your feelings regarding your perception of his lack of empathy. It may be that he is thin skinned and over-reacting, or that he is twisting what you said a bit.
I think I would think what you’d said was critical if said to me in the context you have given. I wouldn’t have stormed out, but i would have been hurt if my partner had chosen a date night to bring up something they are critical about me for, it’s not really the best time.
On the other hand, storming out of the restaurant and now refusing to talk to you today is not a good sign either. If he wants some space to think, that’s fine but he should agree a time to talk it over. Simply ignoring you is not right.
Openly comparing your partner to others is something I would find annoying and hurtful. Stop doing it, it is passive aggressive- whether you mean it to be or not- and is designed to antagonise and/or belittle (even if you aren’t doing it consciously). It is also highly unlikely to engender the change you are looking for.
Equally, on his part if he is actually not upset with you but just twisting what you say to get you off balance, then I can see that that is leaving you second guessing and confused, which is no way to feel in a relationship.
Is it possible that your need for more empathy and compassion are simply not realistic, or at least not from him? I had an ex-partner who needed, from my perspective, quite a lot of emotional support/handholding and it felt like whatever I did was never quite enough/quite right. It was really hard feeling like your partner thinks you just aren’t trying hard enough, didn’t care about them or are being unsupportive when you are trying to be. He felt I was not emotionally available/empathetic as he needed, that I was shutting him out and not supporting him, and sometimes that it seemed like I didn’t care. It was exhausting for both of us. At the time I thought he was overly “needy” and quite hard work, a bit OTT. I;m sure he would characterise me as not especially emotionally open. With hindsight, and some maturing, I realise that neither of us was “bad/wrong” we just were too different in our needs/ways of showing emotional support for us to be able to be in a relationship.
Honestly, this could be one of those situations where two people are simply not compatible as you cannot meet each other’s needs without anyone actually being solely “at fault”.