There are tons of technical differences between the two that experts and enthusiasts could discuss all day. But from an everyday regular-guy standpoint, the primary difference is the handles. The ESEE are more slab-like with a coarse micarta material. The Becker are molded plastic and more rounded. If choosing between the two, I'd suggest seeing them in person and buying whichever is the most comfortable. For the record, I have both.
The wood handle Mora knives, at least the older ones, have a full length stick tang. The Mora knives with plastic handles have partial tangs of various widths and lengths. Neither are a true "full tang" design. You can find online x-ray and take-apart photos for most Mora models to see exactly how long the tangs are, or looking at the available blade kits for sale will give you an idea.