Q:

Should I buy a Canon Zoom Telephoto EF 75-300mm f/4.0-5.6 III or Tamron AF 75-300 mm f/4.0-5.6 LD?

Should I buy a Canon Zoom Telephoto EF 75-300mm f/4.0-5.6 III or Tamron AF 75-300 mm f/4.0-5.6 LD?
which is better choice?

A:

There isn't a better choice among the two lenses you have listed. Your choice is more a case of choosing the lesser of two bad choices.
The EF 75-300mm f/4-5.6 III is likely the poorest performing lens in Canon's current lineup. I would avoid this lens if at all possible.
The Tamron AF 75-300mm f/4-5.6 is not significantly better.
Neither is very sharp, especially on the long end, and both can exhibit fairly strong chromatic abberation under conditions that are condusive to CA. Both are fairly slow to focus.
If you are using an APS-C camera, I would consider the EF-S 55-250mm f/4-5.6 IS II. It can be had relatively cheaply and performs better than either of the lenses you listed. It has optical performance comparable to the EF 70-300mm f/4-5.6 IS when used on an APS-C camera. 

