The gemara says on 31a - אסור לאדם שימלא שחוק פיו בעולם הזה. Rabbeinu Yona interprets it very literally. He writes that some say this has to do with the destruction of the Beis HaMikdash, but if that were the case it would say so explicitly. Rather it is because simcha leads one to get drawn after physical indulgences and forget about doing mitzvos. Based on this he doesn't interpret the gemara which says וגילו ברעדה, במקום גילה שם תהא רעדה, to just mean that simcha should be balanced and controlled. Rabbeinu Yona writes that in the physical world fear and joy are opposites. However, in the service of Hashem, when a person ponders G-d's greatness and develops a fear for G-d, he develops a joy for appreciating the fear he has for Hashem since that fear will ultimately be an inspiration to fulfill mitzvos. This is the type of simcha referred to in the pasuk of עבדו את השם בשמחה, it really means to serve Hashem out of fear, but to develop an appreciation for that fear that brings him simcha. He also considers this to be the peshat in the pasuk of תחת אשר לא עבדת את השם אלקיך בשמחה ובטוב לבב, but direct simcha is not considered positive. However, when the gemara speaks about davening out of simcha, Rabbeinu Yona (22a close to bottom) writes that if one finds himself unable to concentrate due to worries or anxiety, he is allowed to feel simcha for the purpose of inspiring himself to serving Hashem. In short, Rabbeinu Yona considers simcha to be a dangerous emotion, unless it is a result of the service of Hashem, or used as an inspiration to serve Hashem. On the flip side he warns that עצב, sadness or depression is also a dangerous emotion because it leads to physical illness that prevents proper service of Hashem.
Based on Rabbeinu Yona's approach, he explains the response of the amoraim אנא תפילין מנחנא, to mean that when they were challenged for feeling a simcha that is not associated with a mitzvah, they immediately explained that it was associated with a mitzvah and their joy was merely a result of appreciating the mitzvah that they were performing.
Rashi on the other hand doesn't seem to view simcha as something which is inherently bad. The challenge to the amoraim for expressing simcha was that it gave the impression that they were being פורק עול and throwing off the yoke of heaven. To that they respond that the tefillin that they are wearing is a clear sign that they still maintain the yoke of heaven and are not פורק עול. The difference between Rashi and Rabbeinu Yona is that Rashi seems to be concerned with the public display of joy, but the inner emotion is not negative, whereas Rabbeinu Yona is concerned even with the inner feeling of joy.
According to Rabbeinu Yona, nothing changes pre and post destruction of the beis hamikdash. However, the Meiri writes that pre the destruction of the beis hamikdash, simcha shel mitzvah was allowed. Whereas post destruction of the Beis HaMikdash things are intensified so that אסור לאדם שימלא שחוק פיו בעולה הזה even if it for the sake of a mitzvah.