http://www.handyharmancanada.com/TheBrazingBook/Section 1/What brazing is all about/Part 1.htm
Regarding silver brazing: " On non- ferrous metals and steels, the tensile strength of a properly made joint will often exceed that of the metals joined. On stainless steels, it is possible to develop a joint whose tensile strength is 130,000 pounds per square inch. ( 896.3 megapascal [MPa] ). Brazed joints are ductile, able to withstand considerable shock and vibration. Brazed joints are usually easy and rapidly made, with operator skill readily acquired. Brazing is ideally suited to the joining of dissimilar metals. You can easily join assemblies that combine ferrous with nonferrous metals, and metals with widely varying melting points. Brazing is essentially a one-operation process. There is seldom any need for grinding, filing or mechanical finishing after the joint is completed. Brazing is performed at relatively low temperatures, reducing the possibility of warping, overheating or melting the metals being joined. Brazing is economical. "
Brazing strength will exceed base material and weld strength in certain applications. As hard as it is to believe that a nonwelded/brazed application is stronger than a weld, it is possible and commonly used.
Regarding welding:
"It offers one big plus – strength. Properly made, the welded joint is at least as strong as the metals joined. But there are minuses to consider. The joints made at high temperatures, high enough to melt both base metals and filler metal. High temperatures can cause problems, such as possible distortion and warping of the base metals or stresses around the weld area. These dangers are minimal when the metals being joined are thick. But they may become problems when the base metals are thin sections."
Weld strength can exceed brazing strength, but loss of strength can occur in overheating the joint. Temps are easier to control with tig than with mig and generally produce superior joints. The down side to tig and mig is the inability to join disimilar alloys and maintain alloy integrity when the different alloys have different thresholds of structural soundness. A good outcome can be had with tig, but brazing temps are low enough that in most applications, the brazed joint will exceed the weld and base material strength due to protecting the integrity of the base material. The brazing never gets hot enough to remove metal temper. Tig can be used in certain disimilar alloy situations, but brazing is generally seen as being the preferred choice for disimilar applications due to strength, ease of use, and low inout cost, i.e. oxy/acetylene & rods vs. square wave tig setup, etc.
I like welding joints whenever possible, but when disimilar alloys are involved, I'll often braze the joint. Low prep, no clean up, easy fitment. The numbers are sound and the strength remains. Brazing is not for every application, but as honk said, it would be plenty strong for this pin application. I would also propose once again that the Slee pin/bumper combination would be as strong or stronger than a tig weld when properly brazed, (i.e. silver brazed with the proper flux to prevent oxidation), due to the ferrous to nonferrous connection between the mild and stainless steels but honk may be correct in saying that the tig weld would be stronger. This is based on the thickness of the material. Brazing excels in thin materials. Heat and temperature affect thicker materials less, allowing more heat dissipation and fewer potential problems with loss of temper and distortion, leading to a high quality fusion weld.

Either method will work fine.