I transferred at the end of January from another provider, admittedly not CSD, to Vanguard and it all went smoothly.
The Vanguard LS funds I held transferred almost immediately as they were a straight transfer and don't require selling and re-buying.
The non-Vanguard funds I held had to be sold and then Vanguard funds bought with the proceeds. This took ~2 weeks.
Annoyingly, I started the transfer a couple of days before the February dip which meant the funds that got sold were sold quite high! Ah well.
If your question was more about the fees then, yes, Vanguard is a cheaper platform. It does limit you to only Vanguard funds whereas CSD, I believe, lets you buy from many providers. E.g. HSBC, Fidelity, etc.