Yes, and no.
My own Background
I came to TTRPGs via D&D, too. After a brief encounter with AD&D back in the 90s, I really started with 3.5e and if my memories are correct, I haven’t been without at least one D&D group, for the last about 20 years. Interestingly enough, I stuck with 3.5e and just a few weeks ago joined my first group playing 5e. 
So, I think I can compare the two systems a bit.
Just like D&D is “you roll a d20 and add a number to see whether it’s equal or above a target”, STA is “you add the Discipline to the Attribute, then roll a couple of d20s to see whether they’re less than that score”.
Sorry, that’s it, and both games will not change.
So much for the provocative part of my answer. Let’s delve into the mechanics a little bit more.
You’re completely right, yet, I, personally, would argue that STA is even more flexible than D&D. First, in STA, stats are not stats. There are a few rolls that are pretty pre-defined, just like Control+Security for ranged combat, but in essence the roll depends on how a problem is solved in the narrative. Thus, the same problem can ask different characters for rolls on different combinations of attribute and discipline. (Yes, just like there were classes in D&D 3.5e that allowed for adding different attribute modifiers to combat rolls than strength or dexterity.) Add Momentum, Threat, and Traits (esp. Complications) to the scene and you have a metric ton of flexibility for dynamic change.
Some examples: If Commander Lenaris rolls to coordinate the away team for a specific task, he uses his presence/command skill. Lieutenant T’Prel, on the other hand, would use presence/medicine for the same task, using her Doctor’s Orders talent. In case Commander Lenaris would assist her (imagine T’Prel setting up an improvised emergency field hospital for a large group of injured persons and Lenaris backing her up with his authority of rank), she(!) could also re-roll one d20 for free, using his(!) Advisor talent. Or see Lieutenant Commander Zharath: If she wanted to detect an ambush, I would let her roll insight/security against 3 or 4. The same roll would be difficulty 2 or 3 for Commander Lenaris, for he has the Constantly Watching talent.
D&D has spells and feats, STA has talents (a mixture of both, mechanically, if you ask me). See the examples, above. Depending on the narrative (the strategy to solve the problem the character uses in the story) attributes and disciplines to roll, change. Depending on who rolls (and their talents), they change again and/or change difficulties. Some characters are affected by certain traits/complications, some are not (or differently). Yes, a fireball is different than a scorching ray because opponents save against a fireball and the caster tries to hit with a scorching ray. I think the concept of “saves” is not part of STA (I might be wrong, though) and the neares thing are Opposed Tasks, i.e. both roll, higher roll wins. So, yes, combat is different. But, if you ask me, also more flexible than D&D if you use traits in interesting ways.
It would be monumentally arrogant to say that you are playing it wrong. On the other hand, you don’t have fun, so maybe you actually are. 
Anyway, D&D and STA are fundamentally different in their approach to TTRPG. It’s like running and swimming – both are sports that include movement, but you wouldn’t enjoy swimming very much if you tried to run under water (and vice versa). So what you might actually suffer from is trying to take concepts that work well in D&D and use them in STA. It does not necessarily work. Regarding theory, you might want to give the “GNS” Theory by Ron Edwards a read; in my humble opinion, D&D takes a very “gamey” approach while STA focuses very much on the narrative. So it might actually be that you look at STA’s mechanics from an unfavourable perspective.
STA’s mechanics are so simple as they’re not in the focus. Rolling itself is a much smaller deal in STA than it is in D&D because there’s much more focus on setting up the rolls. Sticking with combat (you should follow @Shran’s advice to not focus on combat): Both systems are very flexible, but in different approaches. In D&D you choose between a variety of different “roll set ups”, i.e. you choose whether you attack (scorching ray), the opponent defends (fireball), or you improve a friend’s odds (heroism). In STA you narrate to get a fitting combination of attribute/discipline, how all the different traits have an effect and whether you can apply a Value, or not. Then, you roll, but the outcome is more interesting than the roll itself.
It’s a different philosophy.
Honestly, I can’t tell. Just like @Shran, I always felt more constrained and railroaded in D&D adventures then I do with STA adventures. But your mileage may vary. I, personally, would never use the words “D&D pre-written adventure” and “sandbox” within the same sentence. But if anyone does, I’m happy for them.
The difference I see between D&D adventures and STA adventures is the following: D&D adventures focuses on strategic problems. Defeating a mindflayer is very different from defeating a beholder, a giant, or an owlbear. That’s what the mechanic support well, the rest is roleplay.
STA adventures, on the other hand, focus on moral problems. Is it right to kill the owlbear? Is it possible to reduce it’s natural anger (e.g. via genetic engineering)? Is it right to do so, especially taking into account that owlbears are the result of a genetic experiments, in the first place? And, finally, how to deal with the enraged peasant that took a phaser rifle to kill that frickin’ owlbear all by himself while we were talking out the ethical implications? That’s what the mechanics support, the rest simply rolling.
And if the group finally decided whether to kill the owlbear or to stun the peasant – then it’s no more important which side rolls what. It’s only the final scene, after the story’s been told, after all.