Both schools are highly rated liberal arts colleges; for example, US News puts Amherst at #2 nationally, and Colgate at #16. As these numbers imply, Amherst is usually perceived as more selective and prestigious, but this is like comparing an "A" with an "A+".
The athletic differences are much greater. Colgate plays in NCAA Division I, which is the "major leagues" for college sports. Amherst plays in Division III, which is the "minor leagues". The two schools will not play each other, and won't even have common opponents.
Both teams are currently competitive in their respective divisions. Right now, Colgate is rated #25 in the
Division I poll, and Amherst is rated #16 in the
Division III poll. So they could both make their respective NCAA tournaments. However, the Division I tournament has a much higher profile and a much higher level of play than the Division III tournament.
Amherst is significantly smaller than Colgate, but is located in a large "college town" setting near several other schools. Colgate is larger, but is located in a small town that is relatively isolated.