Mass. Wine Guy, the situation is unfortunately a little more complex than whether one microphone is quieter than another, or whether one recorder is quieter than another. Different microphones have different noise levels, but also different sensitivities (= output level at a given sound level). Different recorders have different noise levels, but also different gain levels (= amount that they amplify whatever you feed into them, including both signal and noise). Microphones and recorders both have overload levels to consider as well.
As a result, unless you do the whole homework assignment with the millivolts, Ohms and decibels, you can sometimes buy the quieter mike and end up with noisier recordings or vice versa. And doing the whole homework assignment is an expression of faith in the manufacturer's specifications, which sometimes is like trusting the purity of swamp water, especially with low-priced, mass-produced equipment. Honesty in specifications is unfortunately one of those things that cost extra in this business.
Thus the most reassuring thing you can read on a board like this is, "I've made many recordings with just that combination of equipment and it worked perfectly well." Otherwise one is left with wishful thinking which come in many varieties and flavors, but is usually at least somewhat misleading.
--best regards