About the dilution of fixer.
In terms of speed of fixation, the optimal concentration is about 120-150g/L of ammonium thiosulfate. However, acceptable fixation may be obtained in 100-200g/L range for film emulsions. Chlorobromide emulsions may be fixed at a bit lower side of this range as well.
Most rapid fixer concentrate products contain 600g or less of ammonium thiosulfate in a liter of concentrate stock, because 600g/L is the practical max concentration. For example, the fixer product I designed, Silvergrain Clearfix (an alkaline rapid fix), contains this maximum amount of ammonium thiosulfate. If you use at the directed 1+3 dilution, you'll get a working solution containing 150g/L ammonium thiosulfate. Even if the fixer gets diluted by carryover of stop bath or rinse water, the fixer remains strong enough to ensure good fixation. If it is diluted 1+4, the working solution will be 120g/L, which is close to "film strength" recommended by Kodak and Ilford.
Because of effort to cut costs and desire to advertise higher concentration, some manufacturers put significantly less 60% ammonium thiosulfate and/or recommend greater dilution to fall in the low end of the usable range. In terms of marketing and commercialism, that may be a good idea, but in my view, it's an unwise approach.
If you use Ilford's Archival Sequence, it's important to use 120-150g/L concentration for one minute. Weaker fixer runs risk of insufficient fixation with 1 min fix, and longer fixing time will require significantly longer washing time to achieve the same residual thiosulfate level (I've tested these things with several materials and several conditions).
Kodak and a few other fixers (such as Edwal Quick Fix) recommend 1+7 dilution for paper. This is more economical if longer fixing time is tolerated, such as small volume processing of RC prints.
As Loose Gravel discussed above, Kodak Rapid Fix (or Edwal Quick Fix for that matter) without hardener may be used in place of Ilford Rapid Fix in Ilford sequence, but at 1+3 or 1+4 dilution.
So, what is the difference between 1+3 and 1+4 dilution? With Clearfix, if you benchmark time to fix a fast film between these dilutions, you may see a small advantage of 1+3. The higher concentration is also a safer choice if you are not very meticulous in removing excess stop bath/rinse water, because even if the fixer gets diluted, it's well within optimal range. But if you are a careful and cost-sensitive darkroom worker, you might want to use an unofficial dilution of 1+4.