Which needle size will give me the longer scarf? I bought two nice skeins while on vacation, and cannot go get any more of the same wool. Now I want to knit a scarf, but I'm afraid it may be a bit too short for my taste, so I want to maximize the length. I want to use a specific pattern and cannot change the number of stitches per row. The length is flexible, it works up to any number of relatively short repeats. 

Under the circumstances, I don't know which needle size to use to maximize length. If I were able to do a fixed width no matter how many stitches it takes, large needles would be a better choice, since I would then have higher rows and use less wool per row. But now that I will be doing a fixed number of stitches per row, no matter what width it creates, I am not sure - if I use small needles, I will get more rows out of my fixed length of wool. 

Can I predict which scarf will be longer under these conditions (fixed stitch number and fixed amount of wool), or does it depend on the exact size of the needles and yarn thickness? 

Update: Swatching is not an option here. I cannot afford to use up my wool on swatches, and don't want to open and reknit because the yarn is on the fluffier side and will probably change after being knit once.

Also please note that I have already made all my decisions about pattern, etc. I am certainly not going to add pieces in another yarn, change the stitches per row, or some other such solution. The only variable I want to change is the needle size, and I want to change it in such a way that the physical length (not the number of rows) is maximized.
Take a yarn in a similar weight, measure out a few yards - knit it with the smaller needles you considered (3mm).
Take that same yarn and measure out the same length - knit it with the larger needles you considered (6mm).

Measure both.

I really think the trade off between "more yarn used in a stitch but taller stitches" on the larger needles and "less yarn used in a stitch but shorter stitches" will be neigh-on impossible to predict without either a swatch or at least physically measuring a stitch.

My prediction is that the larger needles will result in a longer fabric for the same length. This is based on the idea that larger needles = a less dense fabric which means more "air space" incorporated. A smaller needle will result in a denser fabric which means more space filled by yarn and less by air.
This is a theory, please at least swatch in a different yarn.

This may also help. I actually just stumbled on it yesterday:

http://www.knitdarling.com/blog/needle-material-affects-on-gauge

The link contains a summary of an experiment a blogger did on how needle MATERIAL affects gauge. The metal needles made the longest test piece for her and the resin needles made the shortest.