Fallout 4 did a lot of things right in relation to the gameplay but it crippled the diversity of Fallout narratives. It improved upon the loot/inventory mechanics, crafting mechanics (includes base building), customization options, combat/movement mechanics, environmental scale, and AI behaviors. It attempted to streamline the dialogue mechanics but it executed them poorly and within an illogical/linear narrative. I'll give it credit for improving the gameplay but what it did to the narrative fidelity of the Fallout franchise was atrocious.
Overwatch is definitely a unique scenario and coincidentally, I played it again last night after a couple months of neglecting it. Playing Overwatch primarily on console might give me a different perspective on the game but I find that there are a few select heroes that players tend to gravitate towards. Like many of Blizzards games though, it requires constant playtime to maintain a particular skill level. As a result, low-level or inexperienced players are occasionally matched up with dedicated, highly effective players. It won't take as much time jump into than most competitive FPS' but it's definitely a unique title.
Battlefield - I think that we've glorified Bad Company 1/2 a bit too much these days. We should realize that Bad Company and later Battlefield installments play substantially different from one another. Bad Company had more of an arcade-style of gameplay and a substantially lighter aesthetic to its visuals, narrative, and chaotic gameplay. Recent installments try to mimic realism, grit, and more structured gameplay.
For instance, the "levelolution" of previous BF titles created a strange circumstances in online gameplay. Many of the maps were designed with the idea that any building near and blocking an objective would be leveled within a few minutes. It created a very chaotic but limited experience. Without cover, fights were about whomever controlled the open terrain first.
Later installments of BF changed the design to a less destructive but more linear experience. It brought things closer to the chest to make close-engagements more appealing. Limiting the destructive elements allowed a chance for more consistent gameplay but it also dulled things as well. Without the unpredictable destructive elements, you had a more generic (and likely more widely appealing) game.
Frankly, the silver-lining that I've found in recent installments of Battlefield has been in Hardcore servers. Pumping an entire mag or multiple tank shells to kill an enemy is infuriating to me. With Hardcore, every weapon becomes deadly and vehicles become large, moving targets. They can be deadly but they are also not invincible. However, I only prefer Hardcore mode in BF4 or BF1. For some reason, I don't enjoy them in other BF titles.
Dragon Age: Origins is, in my opinion, the better DA game between the three titles. I, personally, despised DA2 and have mixed feelings about DAI. DA:O may have had some clunky gameplay but the narrative depth and efficacy of its story telling mechanics are, in my opinion, substantially better than the later installments. However, Bioware knows that people bond or relate to certain characters more deeply than others so, similar to the Mass Effect franchise, they focus heavily on building a relationship between the player and their preferred companion now. Their games seem to be more about interpersonal stories rather than grand narratives these days. It's not a bad choice but it's becoming a bit stale.
DA:I is surprisingly not as MMO focused as you might think. The issue with DA:I's environment is primarily related to the Hinterlands aka the first area you're placed into. It's massive scale and ungodly amount of side quests takes up maybe 1/4 of the game. I remember the devs making a statement at some point to inform players that they should leave the Hinterlands and come back to it if they're feeling fatigued. For whatever reason, their design of the Hinterlands made DA:I a long haul for many gamers.
Mass Effect - I'm surprised that you disliked ME2 when you were less interested in the MMO style of DA:I. Personally, ME1 is unplayable for me due to its horribly clunky gameplay mechanics. After playing through ME2, ME3, and MEA, I have never been able to go back. Hell, just thinking about all of that generic gear and the Mako exploration sidequests puts me on edge. But similar to DA/DA2, Bioware streamlined much of the clunky mechanics to make a more interpersonal narrative. It removed much of the exploration to make a more linear experience... unless you look at ME:A which is - well let's not talk about that. Actually, let's talk about one aspect of it.
I think ME:A did very well in its (now updated) crafting/inventory system. It incorporated a gear system similar to ME1 without making it feel as arduous. If/when another ME title comes out, I hope the consider reusing that system or some version of it. The system felt more form fitting to the universe, in my opinion.