Although they are similar, Gemini Rising is not the same as Mercury on the ascendant. A planet on the ascendant is more concerned with self expression and a rising sign is more concerned with interpreting and reacting to what is encountered in the world. Consequently, a planet on the ascendant is more noticeable to others than a rising sign.
A person who has Mercury on the ascendant is like a machine you can't turn off. They will talk incessantly. They are obsessed with expressing themselves. Mercury on the ascendant, especially if it is on the twelfth house side, will cause a person to talk about anything that enters their mind. It seems like a constant flow of thoughts that just pour out of their mouths. I'm sure they do have some sort of filter. They can't possibly say everything that crosses their minds, but for the listener, it certainly seems like they do. These people speak as though they are their own audience. What the listener thinks is less important than their need to put their thoughts into words. At their worst, they actually talk to themselves, at their best, they phrase things as though they don't even know the listener. They will refer to people in the same room using the third person. It's as though the power of speech overcomes them and they forget that they are speaking for the listener rather than themselves. Because they are voicing virtually every though they have, they also you the word "I" quite often. This makes sense right? If you are verbally expressing most of the your thoughts and feelings, the word "I" would have to be used a lot. This is the power of the actual planet of Mercury on the ascendant as opposed to simply having Gemini rising.
A planet on the ascendant is more expressive and the rising sign is more receptive. Gemini rising has a different effect. Gemini rising doesn't feel the need to express so much of themselves verbally. Yes, they can be talkers, but they have more restraint. They don't say everything they think. Gemini rising shows itself more by processing what it encounters in the world rather than verbally expressing everything it thinks to the world. Gemini rising looks at the world and wants to analyze and pick things apart. They want to move from thing to thing and they have a low threshold for boredom. Gemini rising figures things out and is critical of what it encounters. Problems are solved by looking at facts and finding concrete answers.
In the end, planets are just more powerful than signs. Mercury on the ascendant is more powerful of an influence than Gemini rising. So, the need for verbal expression may be more obvious.
Also consider that if you have Mercury on the ascendant, you also have a rising sign there with it. So there is always a combined effect of Mercury on the ascendant with whatever rising sign you have. Some rising signs, like Pisces or Sagittarius can really give Mercury a boost. Whereas, with a sign like Capricorn rising, it will be squashed a bit. On the other hand, you can have Gemini rising without any planet contaminating it on the ascendant. This makes a difference because Mercury on the ascendant is never pure like Gemini rising can be. It is always combined with a rising sign. So even though Mercury on the ascendant is more powerful than Gemini rising, you always have to factor in the rising sign with it.