For our purpose here, Time Above Liquidus (TAL) and Peak Temperatures both have the same affect on the solder joint. Look at it as "total heat input", as you can have a longer TAL and lower peak, or a higher peak, and shorter TAL. As it is, together they play arguably, the most vital role of the reflow process. The name of the game is heat. Heat is responsible for solid intermetallic formation and a homogeneous solder joint, as well as proper flux deactivation.
A short TAL or low peak may result in insufficient intermetallic formation, which results in low tensile strength. It is the intermetallic that gives the joint its strength, as you always want the joint to fail during testing at either the board-side of the pad, or in the middle of the solder joint, not along the intermetallic. This is the same for the homogeneity of the joint, which is a metal solution. If the joint is not thoroughly mixed, then it is where the edges of the metal layer is where it fails, which is poor intermetallic formation. Another issue with a short TAL or low peak is not deactivating the flux. Improper flux deactivation causes a multitude of sins, including poor Surface Insulation Resistance (SIR) and continued etching of the metals.
On the flip side, a long TAL or high peak temperature may increase the dissolution of the base metallizations, and possibly increase the MP of the final joint. Too much dissolution of the base metals also forms a higher number and larger of intermetallics. Eventually, this may lead to the complete dissolving of the pad or component lead. Any time you increase the size of the intermetallic crystals, it is easier for them to fracture along said layer. A long TAL or high peak also increases joint stress, again giving another avenue for fracturing.