What is the strongest join for splayed legs?
As is almost always the case with this type of question there is no one clear winner. There are numerous joints — including some unconventional/less seen choices — that would be strong enough, which is all that's needed.
Also, the particular joint chosen would be dictated by the form of the apron (if any) and that is an open question in the overall design of the piece....
In the two images posted neither table appears to use an apron.
In the second if you look closely it seems that there is an X-shaped brace centred on the tabletop, with the legs attached to the end of each arm of the X (maybe with a bridle joint) and then possibly pegged in place, although those could be wood plugs hiding a metal faster of some kind.
In the first it looks like there might be an X-shaped brace also, although flat to the table. Or possibly just a flat plate or flange attached to the tops of the legs. In either case, they could be screwed onto the leg tops from above, then the edges of the X or flange could be screwed to the table from underneath.
Of these two the system in the second image is the stronger option by far, so if the choice were between these two then go with that.
If a more conventional apron is preferred then the apron/leg joint should probably remain what it is most commonly: a mortise and tenon. Somewhat like this:
Note: if the splay on the legs is fairly pronounced I think an open-topped mortise should be avoided here (possibly also a haunched tenon if you want to be extra-cautious). A regular enclosed tenon would provide maximum strength for the forces applied to the joint by the splay of the legs.
Another alternative worth considering is the type of joint often used on commercial splay-legged coffee tables and sideboards:
These rely on a "pre-installed industrial strength fastening system" (just a large threaded insert) so could be strong enough for the legs on a dining table, as they are for quite sizeable sideboards; albeit these have much shorter legs they are substantially heavier than a tabletop, even without things stored inside.