I do both, combined with storage on slants and freezing - what I use all depends on the situation.Interested in whether people are growing starters and then harvesting and storing rather than post fermentation harvest and rinsing? I have been doing this for a while, just bottled a dozen 75 ml jars with Ringwood. Is there any issues doing it this way I need to be aware of? Also, curious about length of viability for these in the fridge - have seen somewhere 3 months?
Reusing the yeast from a previous batch - after rinsing it - is a great way to build up a large number of yeast cells for a lager, strong beer or large batch.
If you have the equipment for storing small samples of yeast (lab-type vials), I see no benefit to splitting and storing a starter, however it is useful if storing the yeast in stubbies, and so can be done without any special containers. I've found that storing washed yeast (which would be the same as a split-starter) keeps it viable for 3-6 months, maybe up to 12 but after that it's usually dead.
If storing yeast I prefer it to be as 'pristine' as possible so (when using a smack-pack or new vial) that's directly out of the pack - simply split the pack into 10 or 15ml sterile vials as soon as it's opened. This way there are as few 'yeast handling' steps as possible, since each has the possibility of introducing contamination, infection or mutation (more chance for this if you make a starter before storing the yeast).
Obviously you need to make a starter in either case (split new-pack or split starter) so having a larger quantity of yeast - from the split starter - is of no real advantage IMHO.
The only time that I store washed slurry for a long period is if there was something interesting about the yeast that I wish to retain. I have reused a recultured Coopers yeast strain in this way for a few years now, because I like what it does and feel it is a 'quick fermenting' strain. However in this case I'm happy for the yeast to change or mutate over time, which is not something that you normally want.