I haven't been able to find the Honda copy you referred to, but I can offer these points.
1. I personally share the fairly popular view that OHV (not OHC) Honda engines are quite distinctly the best available, though they are heavier and far more expensive than Briggs and Stratton engines. Generally, unless you are a perfectionist or an engine enthusiast, Briggs offers better value. (I seem to be both a perfectionist and an engine enthusiast, and own only OHV Hondas.)
2. With the exception of the old 4-height-lever Honda frame, which I think has not been produced in quite a few years, I doubt that the non-engine parts of Honda mowers are better than their competitors. This is especially true of the ones sold in Australia, most of which have poor quality, poorly designed bases which seem to be locally made. My assessment is that the 1980s Rover bases were a bit better, at a fraction of the price.
3. However the Honda-engine-on-an-unbranded-frame mowers I see, have to be viewed with a fair amount of caution. First, be careful that they have GXV (OHV pushrod), not GCV or GSV (OHC belt driven camshaft) engines. The OHC Honda engines are "residential", meaning they are in my opinion greatly inferior in a number of respects. The GSV is said to be "semi-commercial" and the GXV "commercial".
So, are you a perfectionist and engine afficionado, or do you just want to mow the lawn with a reliable, rather smooth-running machine? There are lots of old Rovers with Briggs engines out there for a lot less than $250, that can serve you well. On the other hand, mowing contractors frequently use Honda engines on no-name frames, just like you are thinking of doing, and they do not sell them until they are just as far gone as the genuine Hondas they sell. You should be reluctant to buy one of those for $250. Also, the majority of ex-contractor mowers I've seen are at least beginning to blow smoke due to engine wear.
I suggest you think carefully about what you want, and then think about how you are going to ensure the quality of what you buy.
Post-edit: I have now read the advertisement you were discussing. The seller makes a series of very clear statements which, if true, would mean the mower frame is very similar indeed to a genuine Honda one, and the mower has done very little work. I have no basis for either querying or accepting these statements.
Last edited by grumpy; 15/05/13 08:47 AM. Reason: Add post-edit