In music, as in all the arts, "depth" is a subjective quality dependent on how the audience personally reacts to a given work. Some commentators and music historians have in fact regarded the Baroque era as a period in which composers began more openly expressing emotion. We need to remember, however, that every age expresses itself differently and that our responses are often conditioned by ideas and expectations that are independent of what the artists—whether in music, literature, or painting—intended or felt about their own works. The composers of the medieval and Renaissance periods did not believe that their works lacked "depth" or that a future age would be able to express emotion better or more fully than they could, although this is precisely what some critics and commentators of more recent times have asserted.

The issue of "complexity" is similar, but it can be defined more technically and therefore can be grounded in a greater kind of objectivity. The music of the medieval period (roughly before the year 1400), and the Renaissance (from about 1400 to 1600) is typically heavily polyphonic, meaning that rather than consisting of a simple melody and a chordal accompaniment, the different voices or parts of a motet or madrigal are of equal importance. In the Baroque era (about 1600 to 1750) this is less often the case, though paradoxically the man acknowledged as the greatest composer of the era, J. S. Bach, did in fact write works that are thoroughly polyphonic and have a degree of complexity and sophistication that is arguably unequaled by any other composer in history.

Nevertheless the Baroque era ushered in a stylistic change in which composers sought a kind of simplification that was intended to recreate the assumed characteristics of music from antiquity. Opera was a genre that was self-consciously created in order to replicate in modern form the sung drama of ancient Greece. Composers such as Jacopo Peri, Giulio Caccini, and Claudio Monteverdi produced a new style of opera in which a solo vocal part is typically given a simple instrumental accompaniment, contrasting with the multi-vocal pieces of earlier composers who typified the Renaissance, such as Josquin Des Prez and Giovanni Palestrina.

I would suggest listening to examples of music from these different periods and judging for yourself the qualities that distinguish them. The following recommendations represent starting places for each musical era in question.

• From prior to the Renaissance: Any of the motets of Guillaume de Machaut.
• From the Renaissance: The motet "Miserere mei Deus" by Josquin des Prez and the madrigal "Da le belle contrade d'oriente" by Cipriano de Rore.
• From the early Baroque: Madrigali guerrieri ed amorosi (Madrigals of War and Love) by Claudio Monteverdi.
• From the late Baroque: Any pieces by Antonio Vivaldi, George Frederic Handel, and Johann Sebastian Bach.

More than the later Baroque music, Renaissance era music was more limited in terms of orchestration.  While musical instruments were being invented and refined, there were, quite simply, fewer instruments from which to choose, and the compositions were not necessarily written with any particular instrument in mind.  Consequently, Renaissance era music was routinely performed on whatever instruments were available.  Also, it cannot be ignored that, during the Renaissance period, written pieces were rare given the absence of a mechanism on which to copy compositions -- the printing press was not yet widely -- and there is little documentation on musical compositions from that era.

Because of the lack of written documentation on which one could "read" music, compositions were passed along through demonstrations, which seriously limited the geographic expanse beyond which music could be shared.  

Both Renaissance and Baroque era music were what is known as "polyphony," meaning they used used layered or harmonized melodies, a signature of the more sophisticated style of musical composition that resulted in no small part from the explosion of scientific and cultural creativity that gave the Renaissance period its historical significance.  

When vocals are a part of the composition, which was not unusual, the distinctions between the two eras is more pronounced.  Whereas Renaissance era music placed little emphasis on tonality, Baroque era music used much more forceful and demonstrative vocals.  In addition, the lyrics in Baroque era music were much more precise in meaning than those in Renaissance era music, where lyrics seemed to serve little purpose with regard to any underlying meaning or message.

As mentioned earlier, the Renaissance period had fewer instruments from which to choose when composing or performing, often relying on the omniscient lute.  As time evolved, and newer instruments were designed and introduced into orchestrations, Baroque music became characterized by the increased use of organs, harps, harpischords, and early variations of violins and bass.  Many of these instruments were sparsely available if at all during the earlier period.  

Baroque music reflected the increased possibilities of orchestral arrangements and compositions.  Whereas Renaissance era music tended to remain on a single tempo for the duration of the piece, later Baroque era music introduced much more creativity into the compositions, with tempo changes being a common feature.  Baroque era composers, for example, Bach, Vivaldi, and Handel, were more expressive in their music than their predecessors.

Baroque era music does not necessarily have more depth than the earlier Renaissance period music, but orchestrations were more complex given the expansion in the types of instruments available.  To the extent that it is more complex is a product of the times in which each era occurred.  The Renaissance period ushered in greater creativity, but was technologically more limited.  Given that relative lack of technological sophistication, that the music was as complex as it was speaks to the intelligence of the composers of the time.