The problem is almost never the size itself: tools handle big files fine. What actually matters is how your client receives them. An anonymous link plastered with ads and a 3-day expiry technically works, but it doesn't make anyone want to hire you again.
Compress smart, without breaking your quality
Separate what needs to stay untouched (the high-resolution deliverables) from what can be lightened (previews, contact sheets). For images, a well-tuned web export is usually enough for a selection, so you can save the heavy files for the final delivery.
Avoid zipping everything into one giant file: a client who has to unzip 20GB just to find three photos is one more piece of friction.
Choose a tool built to deliver, not just to transfer
A transfer tool gives you a link. A delivery page gives you a showcase: your brand, a note for the client, download and approval in the same place, and visibility into who opened it.
xFer does exactly that, with parallel uploads for large volumes and private links. You send the heavy stuff without sacrificing your studio's image.
Avoid the traps of free tools
Plenty of free tools pay their bills with ads on the landing page, or force a very short expiry. Check two things: what your client sees when they land, and how long they have to download.
Also always keep your own backup: a delivery tool is never a backup system.
In short
Lighten what can be lightened, deliver on a page in your brand rather than a bare link, and keep an eye on ads and expiry. You send heavy files while staying professional.