Mouser switched to charging VAT up front for UK VAT registered entities sometime in December 2020 as they switched away from using their EU entity and the intra-EU B2B VAT process to using Mouser UK.
Digikey have always charged VAT up front as long as I can recollect.
There's no net difference, as a business you simply offset the VAT each quarter as you'd normally do.
As a small business, the B2B UK => (Non UK) EU VAT accounting anomaly was a minor but not insignificant additional bit of red tape, where, as a business you were responsible for verifying the VAT credentials of your EU business customer before you could issue an invoice with VAT deducted. As such, far from being "frictionless" it was always an additional manual process for SMEs, and it frequently led to delays in shipping for the paperwork and communication to be completed.
I never found an off the shelf eCommerce solution to deal with this automatically, although large enterprises of course have the resources to build their own automated solutions. As it stands now, in 2021, all non-GB shipments are sent out in the same way with the same process, so that old B2B intra EU VAT verification process has now gone.
Whether DHL/UPS/Fedex are the way to go seems to be tribal based largely on anecdotal evidence as far as I can see. Certainly I've stuck with Fedex for my international shipping for a decade now: I understand their systems and I continue to enjoy a substantial discount. I only very, very rarely have any Fedex related problems. If I shifted to another logistics supplier, I'd have to re-learn their systems and rebuild my interfaces. If I were a large enterprise where my volume justified it, of course I'd be putting this out to tender on a regular basis, but as an SME I have bigger fish to fry.
What I would say is that Digikey/UPS deliveries to me seem to be faster than Mouser/Fedex nowadays, although the opposite used to be true say four or five years ago. Digikey/UPS used to be typically three days with Mouser/Fedex a pretty reliable two days. The tables have now turned, Digikey/UPS is two days and Mouser/Fedex three.