Heathrow Express

I’d just get on the Tube at Heathrow. The express doesn’t run as often so you’re waiting for it. Second, you’ll get a seat on the tube guaranteed if you start off at Heathrow.

I'd say the time saved depends on how long you have to wait for a Heathrow Express, personal preference.
You still need to pay for the tube either way (assuming this is not covered by a Britrail Pass). You can use contactless cards.

What you do need to know is how to find the correct tube train at Paddington. Paddington has two separate "Underground" stations, and the one you want isn't actually underground.
When you get off the train in Paddington, you will see stairs roughly level with the middle of the train, going UP to a pedestrian overpass. Signposted "Hammersmith and City line". Go up these stairs and turn right at the top.
Click here for Google Streetview photo.

I’ve used both ways to get to Kings Cross from Heathrow. The tube is simpler with luggage, even if you just have a carryon. By the time I transfered from Express to Tube, there wasn’t that much time saved.

Use the tube. Easier.

Yes, the transfer from the Heathrow Express to the correct tube platform at Paddington is not very convenient, especially with luggage.

I've done this math a few times and the only time I ever found Heathrow Express saves time is when I was staying near Paddington station. If your destination is anywhere near the Piccadilly line, the Tube is quicker (or just as quick) and much cheaper.

Thanks for the feedback. Seems the vote is with the Tube.