How much slower or faster would my bmx bike be if I put a 23t sprocket with a 16t drive?

This depends on what you have now. If we don't know what you have, we can't tell you how much better or worse you'll be.

Here's how you can figure it out though. Basically you are talking about a gear ratio.. Let's pretend you have a 26t sprocket and a 13t drive.

Your gear ratio is then 26/13 which equals 2. So for every 1 time you turn the pedals the wheel turns 2 times.

With the 23t and 16t you would have a 23/16 ratio or 1.43 ratio. With this ratio every time you turn the pedals once the rear wheel turns 1.43 times.

SO what does all this mean? In our example you assume you can move your legs the same speed. So to compare the ratios divide them.. Original Ratio / New Ratio so 2/1.43 so thats 1.398. We can say 1.4 to make it simpler. That means you go 1.4 times as fast with the original.

So that means if you could go 10mph with the 23t and 16t you could go 14mph with your original.

Keep in mind with different ratio's it takes different amounts of strength to go the same speed. This is why mountain bikes have so many gears.

Hope I didn't confuse you.