Hi Darlingbabs - as dangermouse says you can't really compare the two - the synthetic oestrogen in the Loestrin pill (20 mcg ethinylestradiol - not mg!!) is way stronger than estradiol so very much smaller doses are needed for the same effect. As for equivalence - thanks for the confidence Dancingirl but biology doesn't help here!!! Absorption of oestrogen from the different methods is vastly variable between individual women - but I expect there is an approximation out there somewhere, but sorry I don't know what it is!
You can use estradiol to suppress the cycle but it is the oestrogen combined with high doses of progestogen which gives the contraceptive effect, not oestrogen alone eg in Qlaira and Zoely - so theoretically you could use estrogel together with an appropriate progestogen at the right dose - if one was available separately, and licensed. The Mirena coil contains one such....but doesn't always suppress ovulation though.
Hurdity x