Dutch should fit you more because it's aggressive but I would say try both and see which positions you like.
Dutch or Nimzo-Queens Indian
Nimzovich Indian Defence / Queen's Indian Defence: those are top openings.
Dutch is not really sound.

I'm trying to decide between the classical Dutch and the nimzo Queen's Indian.
Nimzo-Dutch!

It's an established fact in the opening forum that the Nimzo-Indian is the perfect defense to 1.d4.
Meanwhile at top level games like the following happen, and not so rare either
Before this game So was having a great tournament in sole lead. It was really a miniature, it was over with 18Bxf7ch. It is a lot of work having Nimzo in Rep, need additional openings for when white plays 3Nf3, 3g3 and white avoids 2c4 etc. The Nimzo itself is a much risker opening than commonly realised.

Play into the gambits they are good fun, white risks over extension and black as per every line in the Dutch still has to be accurate and specific as to their goals.

It's an established fact in the opening forum that the Nimzo-Indian is the perfect defense to 1.d4.
Meanwhile at top level games like the following happen, and not so rare either
Before this game So was having a great tournament in sole lead. It was really a miniature, it was over with 18Bxf7ch. It is a lot of work having Nimzo in Rep, need additional openings for when white plays 3Nf3, 3g3 and white avoids 2c4 etc. The Nimzo itself is a much risker opening than commonly realised.
The same can be said of essentially any d4 response. The NID’s unique challenge is the sheer breadth of positions a Nimzo player must learn compared to the sheer depth of sharper, more theoretical openings. A Grunfeld player may need to learn 5 variations out to move 15, a Semi-Slav player may need to learn 3 variations out to move 25, but a Nimzo player must learn 12 variations out to move 7 and the pawn structures which accompany them.
Essentially every opening has the “challenge” of requiring supplementary openings dependent on an opponent’s response. A Semi-Slav player must be prepared for an Exchange Slav if using the Slav move order or a Catalan if using the QGD move order, along with having responses ready for if White doesn’t commit to placing knights on both f3 and c3 before beginning to develop bishops. A Grunfeld player needs to be ready to transpose to: a KID if White delays Nc3 with Nf3, Be2, and Be3; a Benoni if White delays Nc3 with g3 and Bg2; or a Neo-Grunfeld if White delays Nc3 with both Nf3 and g3.
1… d5 players need to have a response at the ready for the Veresov, BDG, Colle, Stonewall, and London. 1… e6 players need to be ready for the French, the Catalan, the Colle, the Torre, and the London. 1… d6 players need to be ready for the Pirc and the English Rat.
1… Nf6 players need to be ready for the Trompowsky, the London, and the Jobava London.

To take maximum advantage of the Nimzo, you have to be comfortable playing a lot of different pawn structures against different white responses e3, Qc2 etc. Against 3Nf3 the Queen's Indian has the most similar e4 controlling play, but it can lead to some of dullest lines in chess, not very similar to the lively Nimzo at all.
If play something like the Queen's Gambit declined you can play similar pawn structures to whatever white tries. Can get by playing by general principles. (Of course someone who knows some theory as well will do better) Against flank openings like 1c4 , 1Nf3 and others can aim for the same type of position. It's massively less work than trying to include Nimzo in rep. For example 1c4 Nf6 2Nc3 e6 3Nf3 Bb4 has been surprisingly popular in past, but it is quite different play when white delays d4. Also white can play 3e4.
Other Nimzo lose in Sinquefield Cup https://www.chessgames.com/perl/chessgame?gid=2612616 Currently the opening with most loses, two, in the tournament.
@11
"Currently the opening with most loses, two, in the tournament."
++ That is no argument. At least Nimzovich Indian Defence gets played at this top event and Dutch Defence not and for good reason.
The two losses cannot be attributed to the choice of opening.

To take maximum advantage of the Nimzo, you have to be comfortable playing a lot of different pawn structures against different white responses e3, Qc2 etc. Against 3Nf3 the Queen's Indian has the most similar e4 controlling play, but it can lead to some of dullest lines in chess, not very similar to the lively Nimzo at all.
If play something like the Queen's Gambit declined you can play similar pawn structures to whatever white tries. Can get by playing by general principles. (Of course someone who knows some theory as well will do better) Against flank openings like 1c4 , 1Nf3 and others can aim for the same type of position. It's massively less work than trying to include Nimzo in rep. For example 1c4 Nf6 2Nc3 e6 3Nf3 Bb4 has been surprisingly popular in past, but it is quite different play when white delays d4. Also white can play 3e4.
Other Nimzo lose in Sinquefield Cup https://www.chessgames.com/perl/chessgame?gid=2612616 Currently the opening with most loses, two, in the tournament.
Fair. I don’t agree with your assessment, but it is a perfectly reasonable one.
I’d wager that the single best way to improve quickly is to play as many positions as possible as quickly as possible (of course with study, a coach, external practice, and analysis, but I digress), and no opening does that better in the whole game than the NID. It is to d4 what the Sicilian is to e4. Choice and flexibility in exchange for rigidity and comfort.
I could play 100 games as Black (assuming 50 d4 and 50 e4 purely because I cannot be bothered to factor in more variables) and get 5 Barmen Alapin, 5 Nf6 Alapin, 5 Dragon Closed, 5 Botvinnik Centre Closed, 5 Kan, 5 Taimanov, 5 Sveshnikov, 5 Classical, 5 Dragon, 5 Najdorf, 5 QID, 5 Benoni, 5 QGD, 5 Semi-Slav, 5 Tarrasch, 5 Ragozin NID, 5 Noa Mainlines, 5 Nimzo-Dutch, 5 Samisch, 5 Hubner, and 5 Leningrad, or I could play 50 Petroff games and 50 Slav games.
After 1000 games as Black, where I’ve played 50 games in each variation listed above, perhaps I can begin picking lines based on what I do best in and what I like and THEN begin focusing on mastering very specific variations, but at least this way I won’t be well and truly lost in unfamiliar pawn structures as might happen if I’d simply played 500 games in two variations and then started facing opening specialists of sidelines and unfamiliar openings.

I mean, some interesting discussion ITT, but no offense to OP who is 750 rated: you have no concept of how complicated a nimzo/QID based repertoire is and how inapplicable it is to your situation. In the frankly impossible event you learnt a decent chunk of either opening, you would not get what you learnt on the board very often and it would not help much when you did. I am not being mean here, just stating true facts.
The Dutch at least has the advantage that after 1. d4 f5 you have the opening on the board, but you would be way better advised to play d5, concentrate on general opening principles, and forget you ever heard the name of either opening until you are over 1200.
Both are perfectly fine openings until you are absolutely top level but have a very different mindset
1. Dutch Defense tries to directly and actively counter white's first move advantage. It is a high risk high reward opening. Either you win by tactics or attacks or you have a larger chance to get a dubious strategic position
2. The Nimzo on the other hand first tries to neutralize the white's first move advantage and build from there (unless white makes a mistake in his development than you can strike directly). The game generally takes a slower and more strategic direction.
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I'm trying to decide between the classical Dutch and the nimzo Queen's Indian. Note that I am a French defense player so I am not worried about transposing into that. (Meaning I don't have to worry about the Staunton Gambit in the Dutch by playing 1.e6) what is y'all's opinion?