Hello, Natalia. Nice to meet you.
First of all, let me break down the structure of each phrase below;
A. ありがとうございませ -> ありがとうございます
= ありがとう + ございます "Thank you"
B. どもありがとう -> どうもありがとう
= どうも + ありがとう "Thanks a lot"
Basically the difference between those two are 1) the level of politeness and 2) the level of gratitude.
1) the level of politeness: A > B
The phrase A contains ございます, which shows your respect to who you are talking to, while the other does not. Therefore, A is polite, but B is not.
2) the level of gratitude: A < B
The phrase B has どうも, which means "a lot/very much", but the other does not. So the phrase B represents deeper gratitude than A.
In conclusion;
・ありがとうございます is polite enough to say to those who you need to behave: teachers, elders, people at first site, your boss, etc. However, you can't tell how appreciated you are from the text itself.
・どうもありがとう shows a lot of gratitude, but kinda casual that you better say it only to your friends.
Hope this help you.
FYI, you can also say どうもありがとうございます as the combination of both :)