Theoretically, there will be a difference in results between developing 10 shots and 36 shots in the same amount of chemistry at the same working dilution. In practice, I don't think it will be a very big difference unless you are using highly dilute working solutions that contain close-to the amount of minimum developing agent necessary to completely develop the film. In this highly diluted case, the short roll would be notably higher in contrast, as the other 26 shots would not be there sucking as much activity out of the developer as they do in a 36-shot roll. The same thing happens in more standard dilutions, but the difference is very mild. Even when developing the full roll in these cases, there is plenty of surplus activity left in the developer when you dump it. Because of this, when using more standard dilutions, development rate does not slow as much as it does with more dilute developers as developing time passes.
As an example, look at some info about HC-110 developer. Used at the most common dilution, B (1:31 concentrate to water and 1:7 stock to water), and using 240 mL of working solution for one roll of 35 mm film, you end up with nearly 8 mL of concentrate in your developer bath (approximately 7.8 mL). Kodak states that at least 6 mL per roll ought to be used. They state that the average roll of film exhausts about 4 mL of this 6, leaving 2 mL of surplus concentrate per roll, or a 50 percent safety net.
Most people who have done tests will tell you that the minimums stated by photo manufacturers can almost always be safely halved, and full development will be reached. I fully agree with this. 5 mL of Rodinal is more than enough to develop the film completely IME, even though Agfa recommended a 10 mL minimum, just as 3 mL of HC-110 concentrate is enough, even though Kodak recommend 6 mL.
So, speaking of developing a whole roll of 36-shot film using dilution B, you easily meet Kodak's minimums for the amount of concentrate that must be in the working solution. You have over twice as much concentrate in the bath as is used up by a typical roll of film. This large surplus of extra concentrate keeps the developing rate relatively constant throughout the time of development.
Now, let's look at an "unofficial" HC-110 dilution that is used by a good deal of people. It is 1:63 concentrate to water (1:15 stock to water), and is usually called "dilution H." In your 240 mL of developer, this gives you 3.75 mL of concentrate. This is much closer to the real-world minimum needed to completely develop a roll.
Don't be a afraid of using this dilution, though. It will work just fine. It just leaves much less surplus concentrate beyond that which is needed than does dilution B. For example, given that in the real world, you need 3 mL of concentrate to fully develop an average roll, the surplus you have with dilution B is nearly 5 mL, or about 1-2/3 times the amount of concentrate that you need. As was mentioned previously, this large surplus keeps developing rate very constant throughout the developing time, because when developer poops out, there is plenty left to move in and take its place. However, with dilution H, the surplus is only 0.75 mL, or 1/4 times the minimum; in other words, with dilution H, you have about 6x more surplus developer than you have with dilution B. Because of this, much less developer moves in to "cover" the partially used developer, thus development rate decreases more than it does in dilution B, as development time passes. To say this another way, the effect of time on contrast loses a notable degree of the linearity that is achieved with stronger mixes of working solution.
So, take your 1/3 roll of 35mm film and put it through the same analysis. If you need 3 mL to develop an average roll of film in the real word, then you only need 1 mL to develop 1/3 of a roll.
In dilution B, you thus have nearly 7 mL of surplus developer, and nearly 8x more concentrate than you need to fully develop the roll.
In dilution H, you have 2.75 mL of surplus developer, or 2.75x more concentrate than you need to fully develop the roll.
As you can see, with dilution B, you have many more times the surplus concentrate than you have with dilution H. However, even in dilution H, you end up with a higher percentage of surplus developer than you had using dilution B with a full roll. Thus, you have linearity of development rate that is at least equal to what you had with a full roll in dilution B; this is significantly more linear than what you get when developing the full roll in dilution H. Therefore, at a given time in dilution H, you will have more contrast with 1/3 of a roll than you will with a full roll, because development time's affect on contrast in more linear when processing the 1/3 roll than it is with the full roll.
With dilution B, however, both the full roll and the 1/3 roll have plenty of surplus, so both lead to a fairly linear relationship of development time to negative contrast. You don't get nearly as much, if any, difference in linearity between the two.
Just a long winded way to explain what I originally wrote.