It is always tricky comparing a smaller private university like RPI to a massive public like TAMU.
Like in the latest NCES cohort, RPI graduated 602 primary majors in engineering, 69 in EE, which are actually very big numbers for a graduating class of 1379 overall.
But TAMU (College Station) had 13305 graduating students, 2334 primary in Engineering, 270 in EE. When you think about it, being almost 10X the size but only having around 4X in Engineering or EE specifically indicates how this is a real focus at RPI. But still, those are radically different department sizes.
Does that make TAMU a better choice? Obvious not necessarily, indeed colleges like CMU, MIT, and so on are also much smaller than TAMU, but I don’t think anyone would argue that makes them bad choices for kids interested in Robotics! But I think once you are talking RPI versus TAMU, it is more a matter of picking your favorite sort of context in which to study engineering, as opposed to a universal better or worse.
One thing I am sure about, though, is you are not going to be making an obvious mistake either way. These are both traditional engineering powerhouses in their own ways, both are specifically involved in plenty of robotics stuff, and I am sure if you do well at either, you will have plenty of opportunities for relevant internships. And then it is up to you to show that you are a good engineer.
As a final thought, you could try reaching out to the RPI Robotics Club:
It might be interesting to talk to some of those folks and see what they think about Robotics at RPI.