what are the pros and cons of using an enzyme assay kit over immunoblot experiments?

Well, direct comparisons are not easy as there are a host of different enzyme assays, each with different ad- and disadvantages.

In general terms immuniblots can be adapted to all kind of proteins, provided you can get a good antibody, whereas enzyme assays require that the protein under investigation has some quantifiable enzyme activity.

Immunoblots are generally the first step to confirm that your protein is physically "there" (i.e. in your sample/being produced by your system)

Pros:

• Quick and relatively cheap (dependent on how expensive your Abs are)
• Quantifiable if compared against known concentrations of your protein of interest

Cons:

• Doesn't give you any indication of activity, only showing the total amount of protein present
• Heavily dependent on the accuracy of your Abs

Enzyme assay kits are useful if your protein of interest is known/relatively common/a substrate is known.

Pros:

• Usually quick, and very reliable results on the activity of your protein product

Cons:

• Taylor-made to suit your protein product, meaning it has to have known activity (you can of course devise your own assay if you know a substrate)
• Can be more expensive, and usually requires additional equipment (i.e. plate reader)
• Only shows how much of the protein is active, and not the total amount produced

These assays are generally complementary, and it's rare to see a paper without some form of both.