Both forms are very close but there is a very slight difference:

Il faut savoir se comporter en adulte

somewhat implies that the person is an adult (or close enough) and has to behave as such

Il faut savoir se comporter comme un adulte

can be addressed to someone who is not yet an adult.

In the second example, se comporter comme un homme d’affaire suggests the person might not be a businessman, but rather someone who fakes being one (or aspires to be one).

With se comporter en gentleman, the behavior tend to be genuine, innate while with se comporter comme un gentleman, the behavior tend to be artificial, acquired.

Although that’s no indication, “se comporter en adulte” is much more used than “se comporter comme un adulte” ngram.

In the TLFi can be found the following lexicographer’s definition;

[En parlant d’un enfant, d’un adolescent qui prétend agir, se comporter en adulte]

In the light of this usage, one can’t claim that « se comporter comme un adulte » should be intended ony for those persons that are no adults and « se comporter en adulte » for a variety of context including the former. If there is a distinction it must be on an other level.

I’ll submit the following personal insight into the question, without supporting contentions as I can’t find any, and with the simple advice to the reader to remain critical.
The behaviour understated in the use of “en” implies a set of attitudes, that either are not usual for the person considered or that are recognised as typical of what is expected of an adult in a given circumstance; in other words, in this latter case, the form with “en” would be used when it is question of a norm.

• (a) Il n’a que treize ans mais il se comporte en adulte en de nombreuses occasions.

• (b) (Also) Il n’a que treize ans mais il se comporte comme un adulte en de nombreuses circonstances.

• (c) Il s’est fait insulter d’une manière ignoble devant les employés mais il s’est comporté en adulte et a rappelé au diffamateur qu’il aurait à répondre de ses excès au tribunal.

However, we have this;

• (d) Il s’est fait insulter d’une manière ignoble devant les employés et il s’est comporté comme un idiot et a envoyé un coup de poing dans la figure du diffamateur ; il va passer au tribunal pour ça.

Note that in this last example (d) “en” can’t be used; this is generally true, the derogatory term takes “comme”;

• (e) Si vous agissez comme un voleur vous serez traité comme un voleur.
• (f) À agir comme un fou vous n’y gagnerez rien !
• (g) Il l’avait conseillée en homme de foi, sans lui laisser de faux espoirs.
• (i) Pris au piège dans cette sale histoire il avait choisi d’agir quand même en homme d’affaire.

In the example « b », the preposition “comme” seems to be not as relevant for the reason that the behaviour described is not so much considered from the point of view of behaviour that is not usual or merely embraced, but behaviour in strict adhesion to the norms.

Beyond the aforementioned rather imperceptible differences, I tend to find no difference between the two forms.