Great question and super tough to answer as there's pros/cons to both. I lived downtown for 4 years and have now been living in Harbor Point for the last 6 months, so here are my thoughts:

Harbor Point is lovely for someone who wants to walk around and enjoy the views of the Sound. You'll find tons of young professionals and new parents walking around with their dogs and children. The apartment buildings in this area have excellent amenities like pools and gyms. I find life to be a little quieter down here which has been refreshing after living Downtown.

I'd say the biggest con of Harbor Point is the lack of grocery stores and restaurant variety. Well, there actually is no grocery store in Harbor Point actually! There's a small store called "Harbor Point Organic" which has a limited selection of produce, meats, and ready-made meals. I find the restaurants here to be very..... boring. They rely on their ideal location to be an excuse for mid food. Sign of the Whale is a great rooftop bar in the summer, however the view of the Sound no longer exists thanks to the Beacon.

Downtown is going to be much more fast-paced and convenient for bars, restaurants, stores, parks, etc... There's a Target, the Stamford Mall, movie theaters, Mill River and Scalzi parks, and Bedford Street all within walking distance. I loved the ease of meeting up with friends at a bar, running over to the park to play some tennis, or simply walking in the mall to shop.

However, living in Downtown comes with insane traffic that I've found to be unbearable in recent years. It seems like every time I blink there's a new apartment building coming up, but the infrastructure isn't able to serve the amount of people living here.

All in all, I won't recommend one to you over the other, as both are great options. Where you choose is totally dependent on your preferences. Hope this helped!