I guess whether or not something new will sound better depends on how good your current speakers are to begin with, but if your cabinets are starting to deteriorate to the point that they look bad then it mostly comes down to a cost-benefit of looks versus what you are willing to spend for something which, realistically, may only prove to be a marginal difference. I often find that replacing audio equipment for something different tends to do just that-- sound different, but not necessarily be objectively better or worse depending on one's preferences.
I can't give much advice on commercial speakers, but if you are looking for something with a natural sound, the design you linked seems to be pretty well engineered for a flat frequency response, and if it is well-regarded by others I imagine it will sound fine. Intuitively, I don't think the fact that it uses a rear port will be a major issue unless you have it very close to the wall or right up against the corner. That said, I would suspect a front-ported or sealed cabinet design may be slightly less sensitive to placement in the room depending on what you can find.
Personally, I tend to gravitate more towards the bigger, old-school multi-way sealed cabinets as a way to get decent broad-band response just due to size without needing a lot of frequency compensation, but I realize that not everyone has that kind of space to throw around. These days I think a well designed 2-way monitor-type speaker can work just fine, and may be the more practical option in your case. As I said, I am not an expert, so that is a purely emotional and biased preference on my part, mostly due to the fact that it is what I grew up with and am familiar with. At the end of the day, if it sounds good to you then that's all that matters.
If you plan to build something yourself, I will point out that I don't put much stock in spending ridiculous amounts on "audio grade" capacitors and other components in the crossover, and I think altogether too much time gets spent fussing over boutique brands and exotic component materials for the sake of a couple milliohms lower ESR (or worse, components which are attributed vague, near-mystical properties of making your music sound better). I also had to laugh at the author listing all the component values to 6 decimal places, discussing the chamfers on the holes for the speakers, and mentioning the differences in inductance due to adding in the mounting screws on an inductor that is probably rated to a tolerance of +/-10% of it's nominal value anyway. My general philosophy in engineering is to go with a simple, robust design rather than a design that relies on sheer force of precision to hit a particular sweet spot.
If it makes sense within your budget and you want to replace your current speakers, I say go for it. I suspect making something yourself will be less costly if you are worried about spending huge amounts on commercially-made speakers. Once you have something working, an equalizer may also be something to look into, and may not be overly expensive depending on what you are looking for or if you are willing to go with something second hand or not, at least to start out. The general wisdom I have heard regarding EQs is to use them sparingly to make small adjustments to fine-tune the response rather than make extreme changes to try and compensate for flaws elsewhere in the system. I think the problems arise when folks try to set them to huge extremes in a misguided attempt to correct for bad acoustics in a room, or just dial in settings arbitrarily without actually taking any measurements of the room in which they are to be used.