Will a 1.8GHz MacBook Air be much faster than a 1.3GHz model?

Solution 1:

1.3 GHz seems to be mid-2013 Haswell based machine with Intel HD 5000 graphics, the other one is probably mid-2012 Ivy-bridge one with Intel HD 4000.

1. Haswell based CPU is about 5-10% faster than Ivy Bridge according to various benchmarks (so, all in all it should be comparable in terms of pure speed, but read further)
2. Haswell chips make SSD drives run faster
3. Intel HD 5000 is much better than 4000 (and that will give most significant boost to overall performance IMHO)

So, if all other specs are the same, I'd go for 1.3 Haswell one, the problem is that you never know what you'll get when buying refurbished machine.

Solution 2:

You mention newer is 1.3 GHz, but you should look at little closer at the specific processor powering the two Macbook Airs (MBA). You can visit EveryMac and based on the year of the two MBAs determine the processor family.

If you find that the 1.3 GHz process is from the Haswell family while the 1.8 Ghz is from the previous family/generation, you're better of going with the Haswell chip which will yield better performance and power management yielding better battery life from the MBA.