Depends on which Ivy and which major. The Ivies are highly selective but some don't rank even in the top 25 for certain majors. Some of the Ivies are also still a little stuck in the 70s and not particularly welcoming to the military.
Comparing these two schools is like comparing the weather in Alaska vs the weather in Houston in the middle of summer.
I happen to live in CT and have spent time at Yale for various reasons and I also grew up in Texas where many men in my family attended Texas A & M . My father was in the Corp there and went on to serve as an Air Force pilot during Vietnam.
First : Yale has just gotten the ROTC program back after having boycotted it for years.. so it is fairly new with very few participants.
Second: The atmosphere at Yale is VERY liberal vs. the VERY conservative feel of Texas A & M .. Think pro military vs anti military.
Third: Texas A & M has an outstanding petroleum engineering program as well as other engineering programs.... not sure about Yale's engineering ?
Yale is obviously a fine institution and should be considered. When my DS had his NROTC interview and the interviewer saw his stats he asked if he would consider NROTC at Yale.... my DS told the recruiter that he wanted an experience that embraced the military lifestyle ( he has appt to USNA).
If you are interested in engineering, I would pick A&M. It does not appear that Yale even offers petroleum engineering and A&M has one of the best petroleum engineering programs. Mechanical engineering at A&M is also ranked considerably higher than Yale for whatever the rankings are worth.
If your interest is in engineering, I would not choose nor recommend Yale. As a practicing professional engineer, working and living in CT, I know that their engineering programs are not ABET accredited and in my mind that is a significant detriment to their program. If you only have these two schools to choose from and want mechanical, civil, metalurgical, geological, petroleum choose A&M for thier program. Personnally, I would choose NMTech , but then again that's my alma-mater. Good luck on your search and decisions.
Have you visited the campuses????? There is absolutely no comparison. Yale might have a prestigious name but New Haven, CT is not where I would want to send my DS or DD. Of course, I am prejudice - my husband and I both graduated from A&M and our two oldest kids are at A&M now. Our son is a Marine ROTC at A&M. We lived in Connecticut until our oldest was ready to enter high school and we moved back to Texas so I could start the brain washing process to get them to want to go to A&M. Of course she really could have chosen anywhere she wanted to go, but she chose to go there and is finishing her masters this year. My third one broke from rank and will be attending the Air Force Academy - but I guess, he will be happy there too.
Good luck. Don't let the name of a university impress you. A&M has an excellent reputation both in military and engineering.