Please read 
I enjoy both but its really cemented why I love dragon age so much more.
These are story based games set in worlds created entirely for these games. Its common to have discussion about how different story events could have gone differently, or what will happen in universe after the events of the most recent installment. Obviously, how these worlds are set up and how the story is told effects the discussions a lot.
In mass effect society spreads across the galaxy and encompasses trillions of individuals across thousands of planets. Despite that, the major story beats hinge on how you treated individual characters, or whether they are alive or not. Like whether an artificial plague causing 99% of krogan pregnancies to miscarry is justified is completely down to whether the good leader is in charge.
Despite trillions of individuals and complex economics all major conflict boils down to species versus species. All krogan, all asari, all turians are just like that so of course this has happened. There are hints in game that there are many different cultures within each species but we get very little evidence of that, and almost entirely in the 3rd game. Krogan (giant toad people with natural armor, anger issues, and a love of violence) are shown to be maybe not inherently violent individuals that care a bit about others, but thats mostly it. We get one pretty butch Asari (otherwise all feminine species).
So when the community talks about these things its always on individualist or species based terms. It is almost impossible to do materialist analysis because of how the games are made. When the community talks about the game arguments are more heated and personal. There are lots more gotcha type lines than in the dragon age community. I suspect this hostile dynamic could contribute to why there are obviously way more women and queer people in the dragon age community.
Mass effect's story is also about exceptional individuals overcoming impossible odds, which lands way better with men, in general, than women, in general.
In the dragon age community discussions revolve around things like, how does the church use drugs to control their private army? How will giving the dwarves a tool that enables them to put their souls into tanks effect their society? How do independent kingdoms respond to a paramilitary organization run by a prophet encroaching on their land?
Mass effect discussions are, "do the volus deserve a council seat?" Instead of, "How could the Volus get a council seat?" or, "How will the volus having a council seat change existing power dynamics?"
Dragon age stories are, "how does magical talent being both random and dangerous effect society?" "Is it worth it to consort with demons to gain power?" Mass effect stories are, "oo ouch owie my magic gives me migraines." (I like Kaiden don't @ me, the whole child soldier bit both games have is nice)
There are other differences too, like dragon age having braver character writing that scares away some of the chuds. Most people on the dragon age subreddit don't like Vivienne, but understand how her inclusion makes the game better. That kind of subelty doesn't exist in mass effect discussions because the game literally wasn't designed for that level of depth. All characters that are apart of your "squad" are meant to be likeable or at least the kind of person their players would respect. Dragon age release characters also in your "squad" like Sera and Vivienne knowing that tons of their players will hate them.
In summary, mass effect is lacking a pair, let alone a quad. (krogan have 4 testicles) (Please laugh I mentioned testicles)
This is underselling ME3 a bit, it was relatively anti-gamer for its time. ME1 and 2 get the 
tho. Even though I like them anyway.
Edit: how could I forget Dragon age has literally actually good trans representation. Theres a FtM guy whos literally just the coolest fighty bro and his dudes respect him.
"So If I grew up under the Qun they'd treat me like a real man?" "You ARE a real man Krem." 
Edit 2: adding data from reddit surveys
The dragon age subreddit is 45.2% women (3.2% trans), 44% men (1.9% trans), 9.1% non binary and 1.7% other. 45.3% Heterosexual
The Mass effect subreddit is 76.4% men (0.6% trans), 19.7% women (1.5% trans), and 6% total trans people. 73.9% hetero
Dragon age reddit 2023 demographics survey: https://docs.google.com/forms/d/1vi-9XTyIx2kvu4hXb309b0NvdWL7Ub_Yj73le6WXzpI/viewanalytics
Mass effect reddit 2019 demographics survey: https://docs.google.com/forms/d/e/1FAIpQLSdNHQxT7COKRuYIaoHBXt0s3DOdq2RgPCLlJg2RCN5pf3kcKA/viewanalytics
counterpoint: they don't get props for making a black man with an absent father cheat on you. And they clearly tried to make him a likeable character but then just made his romance shitty. He's just boring. Oh! James not jacob. He's boring too and he wouldn't stop flirting with my shepard. He's meant to be shepard's bro guy, they still tried, even if they failed.
Shepard is "the best humanity has to offer." The Warden is the new guy who lived because they were given the boring job. Hawke is a poor refugee who gets caught in some big trouble. The inquisitor got their power completely on accident. Both are individual stories as a consequence of the agency bioware games give their players over the plot. But everyone is literally slobbering on shepards toes the whole trilogy, especially 2 and 3. You get more of that than I'd like in DA, but its way less than ME. Shepard also has big cop energy that DA doesn't.
My point wasn't that there aren't good guys or bad guys. Or that the choices were complex and difficult. Just that what defines your decisions in dragon age games are the systems that individuals are a part of, not the individuals. Curing the genophage good if wrex and eve alive, bad if wreav and no eve. No societal pressures, no politics, economics, just chad wrex putting his species on his back. Though tbf they make it clear eve will end up being more in charge than wrex. They actually cut a pretty matriarchal line with the krogan that I liked.
If you restore the anvil of the void in DA its bad no matter what. Because the power incentivizes unethical behavior.
Yes, the brecilian forest is the weakest part of DAO.
Also, there aren't any compromise koombaya decisions in Dragon Age. At least not that are clearly the best decision. The closest you get is getting briala and celene to marry and rule together in DAI, and getting alistair to marry anora. I chose neither in my cannon playthrough. There are a lot of, "solve the underlying issue if you did things in the right order," though.
I think if you're looking for a big picture non-writing team reason for the difference its that DA games have different protagonists. Everything relates back to your decisions over the trilogy which forces it to be very individualist.
For me its inquisition (with DLC) > DAO > DA2 > ME1 = ME2 > inquisition (base game) = ME3.
Might give Inquisition a go, I was so put off with how much they changed from DA:O I never bothered with the sequels.
This is not my first time proselytizing. Check out these comments from a year ago to get the most out of the game.
https://hexbear.net/comment/3431009
Lol I played DAI at launch so I guess our opinions match. Surprised the DLC could make that much of a difference, honestly.
The Descent is the best dungeon in inquisition. Jaws of Hakkon is the best open world in inquisition. And Trespasser is my favorite RPG experience of all time.