Ilford promotes a fixing sequence using stronger fixer (1+4 or "film-strength") and shorter wash times for fiber-base paper. The thinking behind this is that the shorter fixing time keeps the fixer from soaking into the paper base, making washing easier, thus saving water and time. This is especially true if one uses a wash aid.
This regime works for Ilford papers and fixers, and when the fixing time can be kept to one minute. See here for the details:
https://www.ilfordphoto.com/ilford-optimum-permanance-wash-sequence-fb-papers/ . If the fixing time exceeds the one-minute mark by much (20 or 30 more seconds), then the paper base becomes saturated and longer wash times are needed.
Many of us prefer to use longer fixing times with the weaker, 1+9 dilution for a number of reasons.
Personally, I find it difficult to ensure that my fixing time is not more than one minute. I often bleach prints locally, and have to return them to the fixer once or more times after the bleaching. Also, I use two-bath fixation, and keeping the time down to 30 seconds per bath, especially with larger prints and the longer drain times, is impractical. Using just one bath makes things easier, but reduces the fixer capacity to just 10 8x10s per liter if one wants to process for optimum permanence (see the Ilford tech sheet on Rapid Fixer for the information on this). With two-bath fixation, I can often more than double this capacity, especially if I can promote bath 2 to bath 1 a couple of times, and still have optimally-processed prints and not have a hectic time fixing my prints trying to keep the time down to 60 seconds.
Note also that the throughput capacity for fixers is not affected by the dilution, it is dependent on the amount of dissolved silver built up in the fixer. Therefore, the 1+9 dilution, especially with a two-bath regime, is inherently more economical.
My regime with Ilford Rapid Fixer 1+9 is 1.5-2 minutes per bath, selenium toner, 5-minute water rinse*, 10 minutes in a wash aid, and a final wash for a minimum of 60 minutes. I test regularly for residual silver and residual hypo and my prints pass the tests with flying colors.
*Note: I've been recently reminded that this intermediate wash step before the wash aid is very important and allows the wash aid to do its job much more effectively.
Hope this helps,
Doremus