Looking for comparisons here - if you have both gone in to labor naturally and been induced were the outcomes similar?

Background: I delivered DD at 40W3D, I was scheduled to be induced at 7am but went into labor on my own at 1am after a particularly rough membrane sweep (at my request). Labor was a breeze - as good an experience I could ask for.

Current Situation: Drs office has changed and now only 2 of the 4 deliver. So they have teamed with another practice (7 Drs who deliver) and I will not meet any of them prior to delivery. Meaning 7 of the 9 Drs who could deliver my DD#2 would be strangers to me. Dr has told me that given I had such an uncomplicated birth with DD I could choose to be induced any time after 39w and basically pick a day 1 of the 2 I know are on.

My thoughts are:
-I'd like to think your body responds similar to the natural forces as it would pitocin
-I was 3cm and 80% effaced for the last 3 weeks of my first pregnancy, if that is the case again I will feel much more comfortable inducing since my body is showing signs of readiness
-I'm afraid to rock the boat and maybe the last labor was easy because she made up her own mind
-I'm not sure the Dr really will impact my birth? Does it really matter that much? (fwiw - I am pretty laid back about my birthplan...basically just want a healthy baby and am open to meds)

Looking for others input/opinions/experiences here!