There have been previous threads on this, but for me:
TPE if I want to use TPE Advance ticket discounts or make use of the fact that they post out tickets for free (and allow free modification of Advances through excesses sent by post), plus that it's MixingDeck which can produce 'interesting' journey results
CrossCountry if I just want to book an Advance and be able to change it quickly (e.g. for a train after a meal out), or if I want to be able to use a discount on CrossCountry Advances.
Southern if I want to book walkup tickets in advance (e.g. because I want to ensure that timetable changes don't impact my journey rights), but with the option of a fee-free refund if I don't pick the tickets up.
TrainSplit for researching the kinds of combinations which are optimal, and for booking them when I'm not the one paying the commission
TrainsCanBeCheaper when I want an itinerary to validate a wacky route - as only TCBC has so many via and not via points available! Also when I want to increase the availability of cheap Advance tiers by preventing the use of reservable services where this is avoidable.
And occasionally I will use a TOC's own website where there is a ticket they are selling which they would claim was "missold by the retailer" if I bought it from anyone else! Oh and of course if there's a specific seat I want to reserve on a seatmap (e.g. LNER/VT/XC).