I have not found anyone who asks your interesting question, so I will answer according to my own understanding.

(a) It does not appear that one can simply say that there is a difference between praising the people themselves and praising their habits. This is because the Rambam (Hilchos Avodah Zarah 10:4) writes that "one is not allowed to praise them... all the more so one is not allowed to tell the praise of their deeds or be affectionate of any of their words."

(b) Therefore, it seems to me that one can offer a different solution to this problem. The activities of the Medes and the Persians that the Rabanan praised were not activities that only these nations practiced. There may have been many Jews also who only cut meat on the table, only kissed on the hand, or only gave advice in the field. Similarly, many others may have been modest in the three ways that the Persians were modest. These activities were not necessarily specific at all to the Persians. So Rebbi Akiva and Raban Gamliel were merely praising these activities but were not praising the Medes or Persians at all, as Jews could just as easily practice these good habits and be praiseworthy. It follows that people who heard Rebbi Akiva and Raban Gamliel giving these compliments would realize that they were not praising the Medes and Persians and therefore would not come to learn from their bad ways (which is the reason which the Rambam gives for why one may not praise them).

(c) In contrast, when the Rambam writes that one may not praise their ways, he is referring to activities which are only carried out by these nations.

Kol Tuv,

Dovid Bloom

I found that the contemporary Halchic authorities discuss your question in their commentaries to Maseches Berachos.

1. Rav Elyashiv zt'l, in He'oros l'Maseches Berachos, explains that there is a distinction between praising an entire nation, which is permitted, and praising an individual, which is prohibited. It is permitted to praise a nation if the aim in doing so is to learn from them Derech Eretz and good Midos.

Rav Elyashiv cites the Gemara in Eruvin 110b which tells us how we can learn good traits even from animals. (The Gemara there teaches that even if the Torah would never have been given, we still would have learned modesty from the behavior of cats, the avoidance of theft from the way ants live, and marital faithfulness from doves.) If we can learn good traits from animal creatures, then certainly we can learn them from a nation of the world.

2. Rav Moshe Sternbuch shlit'a, in Pshat v'Iyun on Maseches Berachos, writes that if one merely praises the Hanhagah, the conduct, of the nation, this is permitted, because one is merely pointing out that a certain nation follows a certain behavior pattern, and that such a behavior is praiseworthy. This serves as an incentive for us, because it awakens our hearts to think that if even the Medes can behave in the right way, then we, as a Holy People, certainly have a responsibility to be careful about these matters.

In contrast, one may not praise the activities of an individual idol worshipper even if one's intention is to encourage people to learn from his positive ways.

Rav Sternbuch adds that there is a hint in the Gemara that it is only in these three ways that Chazal admired the Medes and the Persians, which implies that all of their other ways of conduct were not praiseworthy.

3. According to the above approach, the question arises: how was it permissible for the Rambam to praise Aristotle? This question is dealt with in Ashrei ha'Ish (Yoreh Deah, part 1, page 98), a collection of rulings in the name of Rav Elyashiv zt'l. An answer is given there that the Rambam did not praise Aristotle's personality but rather he praised his intellect, which is permitted.

4. It appears to me that the common factor behind all of the ideas mentioned above to answer your question is that if one merely praises a specific habit or good practice of a nation, this is permitted. What is prohibited is to praise the person.

Kol Tuv,

Dovid Bloom

1.

a. I found a good proof for the answer I cited above in the name of the Poskim that Lo Sechanem does not apply when one praises an entire nation. The proof is from the Gemara in Shabbos 33b which relates how the Tana'im once sat together and discussed the Roman government. Rebbi Yehudah opened and said, "How beautiful are the deeds of this nation...." The question arises: why was Rebbi Yehudah not concerned about the prohibition of Lo Sechanem?

b. Rav Moshe Feinstein zt'l in Dibros Moshe (note 92) writes that possibly Lo Sechanem applies only when praising individuals, but does not apply when praising kingdoms. The Rambam (Hilchos Avodah Zarah 10:4) and Shulchan Aruch (YD 151:14) mention only the prohibition against praising them in connection with individuals, not countries. Rav Moshe adds that this certainly is true concerning the kingdoms where we live, since we are obligated to comply with their orders, so it follows that there is no Isur of Lo Sechanem involved.

c. On the basis of our Gemara in Berachos 8b, we have an independent proof to the reasoning of Rav Moshe that there is no prohibition against praising an entire nation.

d. However, it should be noted that the Chidushei Chasam Sofer (Shabbos 33b) does not agree with Rav Moshe's reasoning. The Chasam Sofer writes that the reason why Raban Shimon bar Yochai differed from Rebbi Yehudah was that he maintained that it was forbidden to praise the Romans because of Lo Sechanem. See also Sefas Emes there who appears to disagree with the Dibros Moshe.

2. I also found that your question was discussed by an earlier commentary, Rav Chaim Palaji zt'l of 19th century Turkey, in Teshuvos Nishmas Kol Chai, part 1, Teshuvah 55 (page 244, DH keshe'Ani).

Rav Palaji writes that there is a big difference between the prohibition of Lo Sechanem and the Gemara about the Medes. What we learn from the Medes is similar to the Din of the Torah. The three activities attributed to them represent Derech Eretz and are close to the way of the Torah. In fact, one of these good actions is learned from Yakov Avinu (that he gave advice only in the field).

Rav Palaji cites the aforementioned Rambam, who mentions that the reason why one may not praise them is that this may cause us to learn from their bad ways. Rav Palaji asserts that this applies only concerning non-obligatory activities that they practice. However, if they behave in a way that is similar to the way of the Torah, it follows that there is no prohibition against praising them. On the contrary, it is good to follow their example on such things. If they behave in a good way, and Jews behave less well, this will be a stain on our reputation. In reality, in the first place they learned their good habits from us, as we find that their practice of giving advice only in the field was really derived from Yakov Avinu.

In short, there is no problem with praising the habits of the Medes and the Persians, because the Gemara praises only their good ways which are close to the good way of the Torah.

Dovid Bloom