Both have a main lead who suffered from someone who is in a high position. Both male leads are very similar to their character. Both wish to get revenge and both make it by planing a very long time.
Generally both drama have a pretty similar story, however the biggest difference is the morales the main leads have.

Both dramas are having the same message: when you loose everything, don't give up, there will be a door that opens up. The only difference is that Bonus book finds that with publishing books and Touch is dealing about make-up. Also both have a couple that has an age gap, with Bonus book it is the female that is a bit older than the male, with Touch it is the male that is older than the female. Both pairings work with each other, in both dramas the male leads are the boss, the female leads are their employee. Generally both give off a very similarish feeling.

Just like The Game, Signal deals about murder cases and supernatural occurrences that help investigation teams solve them. While Signal does this with a walkie-talkie that connects the present to the past, The Game deals about someone who can see the death of people. Both try to solve cases with their unique ability. Also both resolve around cases that shape each main character. the cases that shape them are quite similar to one another as well however due to spoilers i cannot go deeper into this.
Signal is a masterpiece of masterpieces, The Game seems to go into a similar direction with it as well.

They both deal about possession and evil spirits and the fight against them. They both have the exact same feeling and same degree of brutality.
They both have characters that have special powers to deal with them.

Both dramas deal about strong females that take revenge on the men that wronged them. Both are very similar in terms of feeling, characters and themes.

In both dramas the male lead is played by Joo Sang Wook. Both deal about a female lead that learned form a disappointment that changed her life and works now together with the male lead to either get revenge, as it is the case in Birth of a Beauty, or to help the male lead, like it is the case in Touch. Both dramas have a very similar feeling and a similar relationship between the leads.

Both main female leads have a special ability that makes it possible for them to help an investigation squad. Both dramas deal about murder cases.

Basically the same main lead with a different skill. Instead of being able to memorize everything, she can see sents. Both deal about murder cases, both have a character who is, because of what happened to them, needing the the person with the special ability.

Both dramas deal about a married couple that has to work out the consequences of betrayal. In both dramas the couples work/are from the same business. Both dramas have strong female leads. Generally the theme infidelity is well developed in both dramas.

Both dramas deal about strong independent, cold women, that have one goal and kind of play a double edged sword. At the one hand they can ruin their company, at the other hand they can bring it to success. Both women are accompanied by males that try to help them with achieving their goals.

Both dramas deal about a group of people that tries to fight for koreas sovereignty. Both are quite powerful when it comes to father land, fighting for what one believes to be right and international relations.
Both dramas have well thought through stories with people that jump between the sides. Also both have quite interesting spies.

Both are crime/investigation/Detective dramas, and both are so very complex and twisted that they leave one hanging at the edge of the seat. Absolute amazement.
There are a few more similarities however due to potential spoiler reveal I cannot name them. There is however a high chance that if one liked the one drama, the other one will appeal as well.