I've finished The Medium a few times now. Let me qualify what I'm about to say by just mentioning that I don't play all that many straight-up horror games, so this take may reflect a certain relative lack of experience with the genre. For example, many people are comparing this game to, or against, Silent Hill and most people seem to consider that franchise the epitome of horror games, but I've only played one Silent Hill game before to date. So yeah, just so everyone understands, I may not have the requisite experience with this particular genre to recognize commonplace tropes that may be present or what have you. It just looked like an interesting game to me and that's why I bought it. With that qualification out of the way...
...Honestly, this game exceeded my expectations the vast majority of the time, especially in the storytelling department. Even despite leaning on your standard issue dude-in-distress set-up (a now-commonplace analogy to the age-old damsel-in-distress scenario often used when a game's protagonist is male), I couldn't help feeling captivated by like the whole first hour of play, especially after meeting Sadness for the first time and despite a bit of a slow build over the next hour and a half or so, things picked up again big time about midway through once you first switched to playing as spirit Thomas and remained highly interesting to me from there on. I was thinking like "WOW, this is one of the best games ever!" until I got to the very last moment of the game and that pretty much ruined the whole thing for me at first. But ya know, as I've pondered it more in subsequent playthroughs and watched explainer videos as well (incidentally here's the best story explainer I've seen in case you've completed the game and still aren't connecting all the dots) I think I'm coming around to appreciating the ending more. I just wish it were more definite at least. I mean reading that lead designer Wojciech Piejko's intention was to impart the message that "there is no universal truth", I guess a subjective ending makes some sense, but...yeah.
The main appeal of this game to me is its story, so I'm gonna have to use spoilers to discuss it further (sorry).
This game is about trauma. Many games address trauma on some level or other, but it's at the thematic center of this one. Specifically, The Medium is about the cycle of violence that trauma often initiates and the nuances involved in understanding why someone may act in horrific ways, and maybe, maybe even forgiving them possibly, without condoning their actions. Video games generally aren't that great at walking that tightrope (and indeed are often particularly insensitive toward topics like sexual abuse and sexual exploitation of young girls), but I think The Medium does an admirable job. One thing the game is very good at overall is conveying the sense of duality that often results from abuse and loss in one's childhood years. In characters like Lily and Richard, we clearly see that the core of their being never matured past childhood as a result.
These and other characters in this game struggle to contain their emotional pain and create separate personalities (in this case manifested literally as spirits) specifically to pour all their pain into so that they can keep going. That's exactly what I do, folks. That's how I keep going. It's why I talk to and argue with myself a lot too. The real question is how one can dispense with that part of themselves without destroying their core, better self in the process. The real answer, of course, is that you can't and you have to learn to accept and even love that part of yourself. Waaaaaay easier said than done! One thing I've come to appreciate about The Medium is that it dares to posit that that's simply not possible for everyone. That's probably not what your therapist will tell you, but it's the truth. I didn't appreciate that painful but honest message at first when I got to the end of the game. I didn't at first at all like the idea that Marianne has to shoot her sister (I mean technically it's subjective who gets shot, but let's get real; this is what's hinted at) who is the cause of the Maw, which is a manifestation of her rage accumulated over a lifetime after being molested routinely as a young girl. My first reaction was like "NO! That can't be what you have to tell survivors of that kind of abuse; like you just deserve to die and should go kill yourself because it made you into a monster? Fucking NO!!" But I've taken more time subsequently to reflect on the different fates of other troubled characters in the game and as much has helped me mentally separate Lily's fate as distinctive to her and not necessarily the best or inevitable outcome of trauma for everyone. Guess I've come to see this as sort of like Spiritfarer for goths.
Marianne also talks to herself even more than I do in a way that demonstrates only finite trust of the player's ability to figure things out for themselves on the part of the developers and I'd complain about it more if I didn't enjoy hearing Kelly Burke's sultry voice quite so much. Troy Baker also just adds a little something extra evocative here too, I think. Speaking of tacit overlap with The Last of Us, I also kinda liked how they "coincidentally" gave Tori a secret girlfriend named Ellie. 
That made me smile. 
. Also, spirit Thomas is an awesome secondary player character! I'm gonna echo the OP's appreciation of the additional edge his sections add.
I loved the cinematic, fixed camera angles, loved the main voice actors, enjoyed the creepy music and the split-screen parts especially, and just find the story imperfect but nonetheless distinctive, needed, and compelling and the main reason to play. Do I want Blooper Team's next game to be a sequel to this one just to tie up loose ends? Nah. I disagree with that sentiment. I'd like to see them continue making genuinely new material. Make a sequel only if there's something of real substance that needs to be added here because the essential mission of this game seems complete to me.
If I have to give The Medium a number, I guess like anywhere in the range of 80 to 90% of perfection seems like an honest score for this game for my taste, depending on exactly how I feel about the ending on a given day, and again based on finite experience with games in this genre to date.
