Oh wow, I'm not sure if I had that exact DBX system (angled bookshelves, sub and sub amp), but I had that or something close to it which was my first "real" system at age 16. Bought it in '93 iirc for $300 back then (yikes!) because a friend's parents bought the same sat/sub/amp system and I liked the idea of satellites and a sub set up which was all the rage with the booming HT and sub market in the early 90's. Ordered via mail order lol.
I haven't listened to it in over a decade, but I kept the whole set up and it's in my basement storage currently.
But, from what I recall, the sats/bookshelfs weren't half bad. Now I was just a teen and far from an "audiophile" at the time, and of course have fond memories of re-discovering and discovering great new-to-me music with my first "real" equipment (before I just had a portable cd player with stock headphones that came with it), but the bookshelfs did seem to have a certain light, airy, and analytical sound which I enjoyed (and still like): pretty sharp, clear, and detailed, with some interesting imaging going on from their unique shape. A bit gimmicky, but the overall sound was good.
And keep in mind that, iirc, the DBX sat/sub/amp setup, while maybe not "hi-fi", was advertised as such in many consumer electronic/stereo mags at the time. It wasn't offered as a mere "cheapo bargain bookshelf system" as the Daytons are, because, at the time, it was not. $300 back then was $440 in '09 dollars according to an online inflation calculator, and either amount is much more, of course, than the Daytons, even with the sub and amp factored in.
Now, of course, times have changed and I believe that one can get, since post 2000 if not 2005, a LOT more speaker for the money than ever before (partially due to ID stores and many smaller companies competing with the big names as well as computer modeling techniques, and better quality material for lower costs, etc.), but still, in early 90's terms, the DBX system was supposed to represent quality while the Daytons, even in today's market where great speakers cost much less retail than before, are not.
Anyway, I've heard that those Daytons are really over hyped and just not very good overall, not "giant killers" or even "entry level hi-fi" by any means. So I've never heard them, but I've heard they are decidedly low-fi with a lot of coloration and boomy mids/mid bass (probably resonance from their cheap construction). Now I'm sure many would also laugh of the DBX bookshelves as well, but, from my memory and the description of the Daytons and all of the above considered, I think you are better off with the DBX's. Jmo though, and, again, I haven't even heard the DBX's in over 10 years and have never heard the Daytons.
One more thing: I did also buy some Infinity bookshelves (for $300 in the mid 90's again!) after I got the DBX's just for a contrast, and, well, I preferred the DBX's. The Infinities, while richer and more balanced, were too colored and veiled for me; I preferred the clarity and lean/angular sound of the DBX's. I eventually replaced the DBX bookshelfs with some JBL Northridge bookshelfs in the late 90's (I don't even know what I spent on those--$250 I think--again: yikes!) because the JBL's had the same kind of analytical presentation as the DBX's but with a fuller and more detailed/refined sound with more bass (6 1/2 woofer iirc). I kept them until my late 20's until I finally decided to start getting into "hi-fi".
So keep the DBX imo, and perhaps also look at the used market for small newish (post 2000) bookshelf/standmounted speakers: Under $50 probably won't get you much, but if you go up to $100 to $150 you can get some very decent used monitors and if you got up to $200 to $300, even new much less used, I think you'd be blown away by many.