Can anyone tell me the differences between these two materials including their strengths and weaknesses?

12L14 and 1045 are SAE standard steel grades, for which the full chemical composition limits are specified in SAE J 403 Chemical Compositions of SAE Carbon Steels.  In the SAE nomenclature the last two digits (14 in 12L14 and 45 in 1045) designate the nominal carbon content in hundredths of a percent by mass.  Therefore 12L14 has a nominal carbon content of 0.14% and 1045 has 0.45%.

The first two digits designate the category of steel.  10xx series steels are plain carbon steels with only Mn, S, and P being specified.  12xx series steels are resulfurized and rephosphorized steels, which means that they have higher limits for the impurity elements P & S (both added for increased machinability).

12L14 is the standard free-machining steel grade.  In addition to P & S, Pb is added to further increase the machinability.  The "L" in 12L14 means it is a lead-containing (Pb) steel.  This steel is usually supplied in cold-drawn bars, which have a moderate amount of strength and excellent machinability, but very poor formability and weldability.  The P, S, & Pb additions also decrease the fatigue and fracture resistance of the steel.  Due to the low carbon content, it does not respond to heat treatments intended to increase strength like Quenching & Tempering, Austempering, etc.

1045 is a standard plain carbon steel that exhibits moderate hardenability due to its elevated carbon content.  It responds to Quench & Temper treatments, but if the section size (wall thickness) is very high, the core will not reach the same strength as the surface.  If it is produced to the same practice as 12L14, say as a cold-drawn bar of the same dimensions, then 1045 will be stronger (tensile yield strength, ultimate tensile strength, fatigue strength), have better fracture toughness, and similar elongation.  It is not generally suitable for welding.  Its machinability will be greatly inferior to 12L14-- using SAE 1018 as a standard of "100", 12L14 is 391%, 1045 is only 55%.

If you have any specific questions that I did not address, please feel free to re-post.  Good luck.