A tele of 2 fixies.

[wrangler_rover]

Last year, I fancied getting a fixie so I bought one which somebody had built up off ebay.
It is a great bike, my son when he first saw it said "Oh no, dad's got yet another bike" but when he rode it, that changed to what a great bike, I'm going to get one. I knew that he would spend a lot more then the £80 that I spent on it so I gave it to him and I decided to buy another one.
After much unsuccessful trawling of ebay, I bought a Carrera Sub Zero from halfords and although it was a shiny new bike, it didn't seem as challenging to ride as the ebay one.
I've looked at the gearing on the 2 bikes and have discovered:
Both bikes are running on 700C x 28 tyres.
Ebay bike, front sprocket: 50 teeth, rear sprocket 16 teeth, drive ratio 3.125 to 1
Carrera Sub Zero, front sprocket: 42 teeth, rear sprocket 16 teeth, drive ratio 2.625 to 1

I want to make the Carrera more challenging to ride so I have thought about changing the rear sprocket to either:
15 teeth, drive ratio 2.8 to 1 or
14 teeth, drive ratio 3 to 1 or
13 teeth, drive ratio 3.23 to 1 (this ratio is possibly too high)
Would changing the front sprocket be a better option?
I would appreciate your thoughts.

[Hypocacculus]

Will a 50 tooth chainring fit your current BCD? If not, then expense makes a smaller sprocket a more attractive option, as well as the fact you wouldn't necessarily have to buy a new chain, assuming the current one is still pretty new.

On the other hand, you might get a bit more mileage out of 50/16. More teeth and chain to share out the wear.

[thirdcrank]

You might find it a bit easier to compare gear combinations with a gear table.

http://www.ctc.org.uk/DesktopDefault.aspx?TabID=3521

In the sort of gear range you are talking about, it's always going to be easier to fine tune the ratio by replacing the chainwheel (front) rather than the fixed cog, as an extra tooth on the back makes 3 - 4 times as much difference as one off the front. (Obviously, that difference varies with the difference in size.)

Beyond that, it's pretty much a question of availability.

[drossall]

The eBay bike would conventionally be described as having an 84" gear (using the approximation of a 27" wheel - for explanation see the gear table above). That's quite large and would often be used for racing. The Carrera has a 71" gear, which is still relatively high. We get various debates on here, and people advocate different gears, but club riders used to spend the winter on 65-68".

It's obviously affected by the speed at which you typically ride, the terrain, and your preferred cadence, but I'd prefer the current Carrera gear, or even go one tooth lower.

Racing, early-season time trials would be on a 72" 'medium gear'. Fitter riders have done 25 miles in less than an hour in these events.

[thirdcrank]

....Racing, early-season time trials would be on a 72" 'medium gear'. Fitter riders have done 25 miles in less than an hour in these events.

I googled Ken Craven and found this insight into the history of UK cycling. Interesting to note that Dave Keeler who came third in the first race reported in the article, a couple of seconds inside the hour, went on to break the End to End record but only held it for a couple of weeks,

http://www.fixedwheel.co.uk/medium%20gear%20history.htm