To me, the two (DEs and open razors) are totally different forms of achieving the same end - being closely shaved. I expect it is the same kind of analogy to which drink you prefer, which car you drive, car or motorbike, roll-up cigarette, tailor-made cigarette, cigar or pipe - all have the same ends but the means of getting there are different.
If I'm in a hurry (which, I admit, is rarely the case) than a DE serves admirably. To me it is a bit like being on autopilot though - it is carelessly easy and the experience is something that leaves little satisfaction. Like the difference between smoking a cigarette or a cigar - the former is quickly forgotten, the latter (if it is a good one, like Mikael's are) is something to be savoured before, during and after the event.
To be brutally honest, getting an open razor as sharp as a DE blade takes a lot of experience, and depending on the formulation of steel used in the open razor it may be quite impossible. And surpass it? I have tried blades honed by nearly all the best exponents in several continents and I couldn't put my hand on my heart and say that any was 'sharper' than a good DE blade. However, given a good steel we can see that the only thing to assess in both DEs and open razors is the bit doing the cutting - the tip of the bevel. If both have equally good steel behind them, then there should be no difference (taking out the myriad little things like poor stropping, poor pre-shave, poor technique, below-par blades, etc, etc) between the two.
If the above holds true, then we have to explore other avenues - nothing is as simple as it seems, and better-informed people than most of us have been arguing the same issues as us for generations with no consensus of opinion: controlled experiments carried out by highly qualified technicians under the control of eminent scientists have been undertaken, but what should be black or white still appears to be grey, though.
One avenue explored is the thickness of the blade. IMO that does not count - the bevel is doing the cutting. Another is the coating applied to DE blades to allow them to 'slide' and give a smoother feeling in use. Another is what we really mean by 'sharpness' - to many this is the critical issue. DE blades and disposable blade open razors give a really sharp shave (although this is in line with what frameback open razors give) which can be uncomfortable and cause 'weepers' and irritation. Open razors generally do not exhibit this quality - they appear to give a smoother, more forgiving shave. That's only my opinion though - I'm no scientific expert, all I can base this on is my own skin type, hair type, preparation and the many hundreds of open razors and DEs I have tried.
There are other factors to consider, too. For instance, does stropping (especially on a pasted strop) - contribute to a secondary bevel that is more obtuse than the bevel straight of the hone for an open razor? Disregarding burrs, it certainly does something: the slightly too-sharp feeling tends to go away after the second or third shave with an open razor, and I believe that this is intimately coupled with stropping, having stropped a few razors for far longer than necessary to induce the feel of the 'third shave' without having to have shaved three times.
Cheapness of an open razor compared to a DE? That's a bit of a poser. You will need a selection of hones - expensive. You will need a decent strop - expensive. Then there are pastes, powders, different stropping materials, paddle and hanging strops to try, oils for both razor and strop to consider, diamond compounds to try out and most of all IME - the overwhelming desire to own yet another open razor. I could kit-out my Fatboy with enough blades to shave my whole body until the day I die for less! Compound disposable blades might push it a bit, though!
In the end analysis. I don't think it is a matter of which is best, but which you prefer. Accept that, and you can then sit back and let others tackle the technical dilemmas. My choice is an open razor.
Regards,
Neil