Intriguing question. I see the stigma felt by HIV/AIDS sufferers as a subset or spin-off from that felt by the homosexual community. Prejudice towards both these groups seems to be progressively lessening, if ever so slightly. In the US there is growing public support for same sex marriage and the once irrational fear of HIV/AIDS patients seems to be subsiding as medical treatment has become available and fewer cases (in the US at least) are reported. Also some decline in stigma towards those with HIV/AIDS may have been influenced by reports of cases in the "straight" community due to bisexual partners, tainted blood supplies, or exposure not involving sexual contact. On the other hand, speaking only from a US perspective, I see little weakening of the stigma towards mental illness or, for that matter, suicide. If anything it appears to be periodically enhanced by media overkill (poor choice of words) on stories of multiple shootings involving individuals known/suspected to have untreated/under-treated serious mental illness. Lastly, the public may have come to regard HIV/AIDS as a "medical" or "public health" problem while mental illness is still seen as malingering or a character flaw. So my read is that the stigma towards mental illness is far currently more virulent than that towards HIV/AIDS.
Unfortunately, stigma in relation to HIV is alive and well. Gay men living with HIV are stigmatized by other gay men ("gay on gay shaming"), by society at large, and by public health professionals. People living with HIV continue to lose their jobs because of their HIV status and some have even been denied medical and dental care. HIV criminalization, which perpetuates stigma, continues to be a huge issue throughout the US for people living with HIV. There are also many people living with HIV who dual or triple diagnosis. Having HIV, mental health and a substance abuse diagnosis.
Stigma towards persons with HIV persists, but in the US, it has lessened over the three decades of the epidemic. Reasons I can think of for the reduction in stigma over time include declining HIV incidence, effective treatment, diversification of persons getting infected, and greater tolerance of different groups that have been heavily affected (e.g., gay men).
That said, I'm curious why you're seeking to compare stigma against HIV with that against mental illness. The first is a specific infection, the second a range of conditions, so they're not especially comparable in that sense. And why compare at all? Both are stigmatized, and people with either condition deserve respect and access to care. Are you interested in how anti-stigma activism comes about for each? Maybe existing activism networks among affected people, and homogeneity among the affected, actually support anti-stigma efforts in some sense. Those conditions were present in the gay community in the early days of HIV but perhaps do not exist to the same extent among persons with mental illness.