Canon 55-250 f4-5.6 IS STM or 70-300 f4-5.6 IS USM(The 2005 model)?

[totallyastick]

I'm looking to purchase one of these lenses as an upgrade to my kit 75-300 which is quite soft. Which of these has better image quality? I will also be using these for birds, and will probably finding myself cropping many pictures, even more so with the 55-250. 

[Tronhard]

I would encourage you to read the following article I published on the EF 70-300 range:
70-300 Canon Lenses In-Depth Analysis - Canon Community

As a wildlife photographer I would recommend the EF 70-300 for precisely the reasons you mention.

[totallyastick]

Thanks for the response.

How is the focus on this lens? 

[Tronhard]

The lens focuses well.   Much depends on how you configure the camera to do the focusing.  Over the years I have found that the following is very effective:

Focus is set to single point centre focus.  By default area focus will seek the closest point to focus on, which is not the eye of the subject, but may be a stone, twig or nose.  Single point focus allows much more precision.
Focus is set to Back Button Focus on the AF-ON button with Servo Auto Focus:  See this film from Canon on the benefits and setup of this configuration:

Finally, single point centre metering assigned to the * button:  Evaluative metering tends to average out the whole area and make that the value for setting exposure.  However, that is often not accurate, as in the case of high-contrast scenes or backlit  ones.   Also, if the subject is naturally very dark or very light (thing polar bear or black bear) the camera's averaging will either under expose them or over expose then respectively.   So, I use single point metering on the centre point to pick an point of 18% reflectance - mid grey (although colour is irrelevant), which is what the senor is seeking.

So, how does this work:
1. find the point on which to meter, put that on the centre of the image and lock with the * button
2. point the centre on the eye of the subject and lock with the AF-ON button- if the subject is still, just tap the button, if the subject is moving hold it down.
3. recompose and press the shutter button to take the photo.

If it seems complicated, that's because it takes so long to describe.  With practice, this can take about a second.  Here are some results using this method:  all shots taken with the lens in question, hand-held, available light.  I chose these because the images are contrasty and posed focusing challenges.  The image of the carving, in particular, gives some clue as to the quality of resolution.
60D, EF70-300@300mm, f/5.6, 1/400sec, ISO-1600  60D, EF70-300@300mm, f/5.6, 1/100sec, ISO-160060D, EF70-300@300mm, f/7.1, 1/200sec, ISO-1600  60D, EF70-300@225mm, f/5.6, 1/400sec, ISO-160060D, EF70-300@70mm, f/5.6, 1/20sec, ISO-1600  60D, EF70-300@105mm, f/5.6, 1/20sec, ISO-1600

In this last image, there is a lot of contrast from light and the plumage, the bird is moving and the eye is well off centre but still sharp.

650D, EF70-300@160mm, f/5.6, 1/500sec, ISO-200