“Anybody who knows them both would not mention Dietrich in the same breath as Garbo. Garbo gets her effects from herself. All the director has to do is to lead her gently along, and she will do the rest. But Dietrich is all director. Her work conveys the impressions of a man with a gun – standing over her, forcing her through every action, all the time.”

Marlene dressed full six months as a man in Blonde Venus before Greta Garbo did the same in Queen Christina. Garbo always thought that she and Dietrich were quite different. It was obviously the controversy Marlene stirred up while dressed in a tuxedo, whereas Garbo liked to wear men's clothes temporarily as she found them more practical and comfortable.

 
“(Marlene Dietrich is a) symbol of glamour like whom there is but one other in motion pictures, and when you see 'Morocco', you will be reminded who that is.”

 
The New York Times wrote: “Marlene Dietrich, German star who is now in Hollywood, will be given an early opportunity to show whether she is the long sought rival for Greta Garbo. According to present plans, Miss Dietrich is to be starred in a film based on the life of Mata Hari, which is also the subject of Garbo's next.”

Film on Mata Hari

It was common knowledge that Paramount had completed Morocco, Dietrich's American debut. However, the mention of M-G-M's Mata Hari project, which had been in script development since May 1930, was a surprise.  So was the proliferation of posters heralding Dietrich as Paramount's Great New Star.

"Marlene Dietrich Expected to Become Screen Star Overnight” was the headline seen in numerous New York newspapers. Paramount, guided and goaded by Dietrich's autocratic director, Josef von Sternberg, was spending a great deal of money to acquaint America with Dietrich.

The question, both spoken and unspoken, since no one had yet seen her in The Blue Angel, was if she could really pose a threat to Garbo. On November 14, 1930, Morocco premiered at the Rivoli Theatre in New York. Within a week, it was breaking house box-office records, Dietrich was getting raves, and Sid Grauman's Chinese Theatre was planning to pay Morocco the Unprecedented

What did Marlene think about the reviews?

Not surprisingly, Dietrich was distressed by the constant mention of Garbo in her reviews . “If they had only shown ‘ The Blue Angel' first,” said Dietrich in a Los Angeles Times interview, “then people would not say these things. There I was not a very nice girl, a little tough. I was not like Garbo. I was myself. In ‘ Morocco' it is different. Maybe I do look a little like her, but I don't try to. If I do, I can't help it, and I think that it is cruel of people to say such things.”

The alleged resemblance went back as far as Dietrich's 1929 German film Ich Küsse Ihre Hand (I Kiss Your Hand, Madame).

"Why has she been given the coiffure of the Swedish star?” asked Harms G. Lustig in Tempo magazine. “Why has she been put into Garbo's clothes? True enough, this German girl (who has really not all that many German characteristics) has a similar and curiously alluring expression of immobility and indolence.”

Though Garbo most likely read all this, her only comment on her would-be rival was a disingenuous “Who is Marlene Dietrich?”

Clarence Brown on Garbo's dangerous rival

“They do say, Mr. Brown, that Marlene Dietrich is going to be a dangerous rival.” “Anyone who knows them both,” answered director Clarence Brown, “would not mention Marlene Dietrich in the same breath with Greta Garbo, who gets her effects from her own mind.

All the director must do is indicate the way and she follows it unerringly. Dietrich is all director. Her work gives the impression that a man is standing over her with a gun, forcing her through every action, all the time.” Brown

“She is unique.” A fan letter said, “Marlene Dietrich has everything that Garbo has and something else besides–humor!”

Richard Watts Jr. in the New York Herald Tribune wrote: “ Her hasty rise to film celebrity was the result of neither luck, accident, nor publicity. Her almost lyrically ironic air of detachment and, to be as frank about it as possible, her physical appeal, make her one of the great personages of the local drama.”

In addition to this physical appeal, there was Dietrich's ability to put over a song. If she meant to eclipse Garbo, she was qualified to do so. Thus, it was not enough that Garbo's next film flout the depression. It also had to put Dietrich in her place– second place. To accomplish this, Garbo would once again have to portray a “bad woman,” even if it meant a slight variation on her formula.

Before Garbo's Mata Hari began earning its impressive profits, MGM had to acknowledge that Paramount's answer to Greta Garbo was not doing so badly. Marlene Dietrich's first three films with Josef von Sternberg (The Blue Angel, Morocco, and Dishonored) had brought Paramount a profit of more than $2 million. These exercises in style did have detractors.

"I didn't know whether I was looking at a spy drama or a hosiery show,” Photoplay's Leonard Hall wrote of Dishonored. “I couldn't see the genius for the legs.” Not surprisingly, Adrian made sure to expose Garbo's legs as often as possible in Mata Hari.

Source
Greta Garbo: A Cinematic Legacy – by Mark A. Vieira

Mercedes de Acosta wrote in a 1934 letter to Marlene Dietrich:

“I do know that I have built up in my emotions a person that does not exist. My mind sees the real person – a Swedish servant girl with a face touched by God – only interested in money, her health, sex, food and sleep.

And yet her face tricks my mind and my spirit builds her up into something that fights with my brain. I do love her but I only love the person I have created and not the person who is real.”

By her own account, Mercedes de Acosta did not waste any time finding consolation after Greta left. She wrote of meeting Marlene Dietrich at a performance by dancer Harald Kreutzberg.

Not so according to Maria Riva, Dietrichs daughter. “My mother told me she found her sobbing in the kitchen during a party at the Thalberg's house. This kitchen meeting had many versions but always ended with the ‘cruet Swede' being replaced by the ‘luminous German aristocrat,'” Riva said.

 Marlene herself, who was distressed about the steady comparisons, during an interview given to Los Angeles.

"If they had only shown 'The Blue Angel first' ,” said Dietrich in a Los Angeles Times interview, “then people would not say these things. There I was not a very nice girl, a little tough. I was not like Garbo. I was myself. In Morocco it is different. Maybe I do look a little like her, but I don't try to. If I do, I can't help it, and I think that it is cruel of people to say such things."

Garbo's comment during the same time

 
Garbo wore her dark glasses because the light hurt her eyes, which were sensitive, and not just to cover up her face. I recall seeing her on Fifth Avenue with Gayelord Hauser at the corner of Fifty-fifth Street.

Some woman walked up and said , “Oh, you're Greta Garbo !” and she looked down and just said, “Yes.”

She didn't have the elegance of Marlene. I never saw a woman handle a crowd the way Dietrich could – she just hypnotized them. GG couldn't do that, but if somebody got close and said something to her politely, she was nice. She'd say , “I must go, you know, I have to leave,” something like that, and then disengage.