2- solvation effects, in water solution, the bulky t-Butoxide ion is more difficult to solvate which destabilizes it relative to ethoxide. Plastic surgeon shares one weird way to fill in wrinkles at home. Beverly Hills surgeon reveals at home fix (no creams needed).
In (CH3)3C-OH, the conjugate acid of the tert-butoxide ion, the +I effect on the alcoholic carbon is three times that in CH3-CH2-OH, the conjugate acid of the ethoxide ion which has only one methyl group. Therefore, the O-H bond in tert-butyl alcohol is less polar than that in ethanol, and the former should be a much weaker acid than the latter.
However, t-butoxide despite being a strong base is sterically encumbered. Therefore, is it not a suitable nucleophile due to its bulk. It cannnot substitute—It eliminates in concerted step. For the same reaction, a smaller nucleophile does the job best.
Because of more Lewis basicity of ethoxide due to more electron density on oxygen in ethoxide (inductive +I effect of ethyl group) as compared to hydroxide ion, ethoxide is better nucleophile. Here, in this case order of nucleophilicity and basicity is same but this is not always true (This is due to steric reasons, etc.