If a bridge is not at the same level as the rest of the piece, should it be preferably at a smaller or larger level ? Both cases seem to exist but it is difficult to establish a preference by ear. Does it really make a difference ?

     We gather that by change of level, you mean change of Level 0. Yes, it makes a difference and the preference is at a larger Level 0. When a change of Level 0 is made from a smaller to a larger level, the breath between the two sections (the length of the Beat at the end of the first section) is deeper than when a change of Level 0 is made from a larger to a smaller level. There is therefore a tighter bond between the two sections in this second case, the larger level section acting as an antecedent and the smaller level section acting as a consequent. This is why a bridge (indicated "B") should be at a larger Level 0 since it acts as antecedent to the final "A" section, whether the form be the complete AABA or the ternary ABA.
     Now, why is it difficult to establish this preference by ear ? Because bridges are usually at a fairly large rhythmic level and intuition does not function as reliably at these levels. Bringing the whole problem down to a smaller level would enable us to perceive the situation more easily. The French song J'ai du bon tabac has a very pertinent Melo-rhythm which goes // , / // , where large Level 0 bar-lines are indicated double, small Level 0 bar-lines are indicated single, and the two phrases (antecedent and consequent) are separated by a comma. Using the antecedent // as a bridge (B) and the consequent / // for the 3 "A"s, the complete AABA would be / // , / // , // , / // , certainly a more satisfying combination than the opposite // , // , / // , // . It would be helpful to Footsie these examples, changing Level 0 as required, to really feel what this is all about. Gradually slowing down the tempo would help develop the feeling for larger levels.
     Let's get back to the Melo-rhythm of J'ai du bon tabac and examine it more carefully. The antecedent // is composed of only 3 s and the consequent / // is composed of 5 s, not 4 s each as might be expected. This is caused by the fact that the last note of the larger level antecedent is shortened by the pick-up kind of entry of the smaller level consequent, and the last note of the smaller level consequent is lengthened by the entry of the larger level antecedent on the repeat of the passage. At this small intuitively reliable level, two even groups of 4 s, // , / // would seem quite awkward, destroying the larger Level 0 of the antecedent.
     Now let's transpose this to a larger level, where the "A"s and the "B" are 8 bars long (a fairly standard length) and see what happens on each side of the bridge (before and after it). (a) If the bridge is at a smaller Level 0 (as in Santa Claus Is Comin' To Town), the last note of the second "A" will be a bar shorter, reducing the section to a 7-bar length, and the last note of the bridge will be a bar longer, augmenting the section to a 9-bar length. (b) If the bridge is at a larger Level 0 (as in Over The Rainbow), the last note of the second "A" will be a bar longer, augmenting the section to a 9-bar length, and the last note of the bridge will be a bar shorter, reducing the section to a 7-bar length. Unfortunately, in each case (as is the habit), all the sections maintain an even 8-bar length, and the bridge is placed one bar too late in the first case and one bar too early in the second case. One should not be surprised that, under such misleading conditions, evaluation of preference for smaller or larger level bridges might be intuitively difficult.
     This is a very good question, but certainly not an easy one to answer. Let us know if you need more clarification.