The words have been around hundreds and hundreds of years. While they were constructed by combining awe with -ful or -some, once they became lexical items as complete words, their meaning was able to drift like any other lexical item — the fact that each word is composed of a stem and suffix doesn't stop this. (Also, bear in mind that -some, the suffix, doesn't mean "some of X", it means "having the quality of X". Think fearsome, loathsome, cumbersome. And -ful is basically the same as -some in its meaning, with all words.)
Originally, awful had the meaning of being awe-inspiring (including positive connotations), as well as "worthy of, or commanding, profound respect or reverential fear." It was not a far stretch to then use it also to mean "Causing dread; terrible, dreadful, appalling." The earliest records of these uses date back to at least 1000 AD. Between 1000 and 1800, the word evolved to the current meaning: "Frightful, very ugly, monstrous; and hence as a mere intensive deriving its sense from the context = Exceedingly bad, great, long, etc."
Awesome came around much later than awful. It is first recorded in 1598, after awful had been around hundreds of years. Perhaps the need for this word arose because awful had already taken on such a strong negative connotation by this time. So awesome stepped in to again have the meaning of "awe-inspiring", but without the strong negative connotations. Ultimately, in the mid-1900s, the word awesome went from awe-inspiring to its more common use today: "amazing, great, etc."
So, this is how the words ended up like this. Yes, you do have to memorize the words to some extent, because they have certain connotations and colloquial meanings that are extremely common. But, again, part of the problem is treating -some like some. None of the -some words have a connection to the current meaning of some.
(All of this data came from the OED.)