Ah, a really tough question, why indeed? I too have tried to think about these reactions. I think that t-butoxide is a stronger base due to the electron donation of the methyl groups. I think that in comparing t-butoxide with methoxide or ethoxide one might expect t-butoxide might be faster. Another factor, though one I cannot corroborate, is the effect of the solvent. Reactions of methanol or ethanol probably are all in the alcohol as bulk solvent. That cannot be the case for t-butoxide.
I am familiar with the steric argument, though I have difficulty in understanding it. If I assume the stereoelectronic requirement for a reaction with an alkoxide is linear, then I cannot see how t-butoxide would be more sterically demanding than methoxide. The reaction of an acetylide with a secondary halide gives elimination. Acetylide is generally regarded as having a low steric demand, though a more basic reagent. This begins to make me think the basicity may be a bigger issue than a steric argument. (I am only saying this in trying to understand the chemistry, if asked on a test, the correct answer is 'steric'). In my book, I used the ratio of substitution to elimination for a reaction of t-butoxide with 1-bromooctadecane. The major product is elimination, but substitution also occurs.
I focused on the differences in elimination reactions. I thought that Zaitsev elimination reaction products were E1-like even though E2-kinetics. I argue a neighboring carbocation would allow a shift of electrons from the most electron rich carbon would give the most substituted alkene. A similar analysis of a Hofmann elimination may leave one to think that an ammonium salt would be less electron withdrawing than an equivalent bromide or iodide, less carbocation-like and that would give a Zaitsev product. In that case, the elimination can seem to be more dependent on the CH acidity and give the least substituted alkene.
The best example I could find with t-butoxide v ethoxide is the reaction of 1-chloro-1-methylcyclohexane. Ethoxide will give 1-methylcyclohexene, the Zaitsev product. t-Butoxide will give methylenecyclohexane, a Hofmann product. Bromo and iodide give mainly the Zaitsev product. I reason that chloro is less electron withdrawing and can allow the reaction of t-butoxide to discriminate favoring the acidity of the CH3-group leading to the methylenecyclohexane.
I realize I have not and cannot answer the question directly. The best I can do is to report on some of the differences I have found. Questions of A gives B and C gives D are difficult to correctly analogize. In my manuscript, I have dealt with similar problems and have reached different opinions that one might have found in textbooks. I don't think one can make a direct comparison. How does one gauge the effect of the change in solvent for example? How could a solvent change the effect of the reagent?