Latent Class gives you utility scores and importance scores for classes (segments) of respondents. The number of classes depends on how many you as the researcher requested.
Let's give a simple example for how a single class (segment) could entirely miss the true importance of an attribute. Let's imagine that you have a two-level attribute for brand: level 1) brand A, level 2) brand B. Let's say half the respondents prefer brand A and half prefer brand B. If you pool all the respondents into a single class (aggregate logit analysis), then it will look like there is essentially no difference in utility on average for brand A vs. brand B. The importance score (reflecting the range of utilities for brand) will appear to be zero for brand, even though respondents may think their preference for either brand A or B is quite important to them.
Of course, with Latent Class, you can tell it to find two groups of respondents rather than one and it's quite possible that those two groups will break out strongly based on brand preference for A vs. B. But, you can see that other attributes might have more than just 2 levels and there are multiple attributes that vary independently in a conjoint exercise. So, even a 5, 6 or 7-group solution might not be able to accurately isolate and figure out the separate importance scores for each of the attributes.
On the other hand, HB estimates utilities for each respondent. So, the attribute importance is calculated individually for each respondent and the aggregation problems that can damp the importance for attributes where respondents differ in their tastes can be reduced.
However, all is not perfect with HB. Attributes that respondents completely ignore can still take on some attribute importance by virtue of random error or variation in the individual-level utilities. That's because the importance calculation takes advantage of any difference in utilities within an attribute, whether that difference is real or just due to random noise.
That said, HB is generally preferred for better assessing the importance of attributes via the traditional "importance score" calculation. We should note, however, that importance score calculations can be strange to work with and easily misinterpreted. We prefer to assess the impact an attribute has on choice through well-positioned market simulation scenarios and sensitivity analysis.