Hi V8chewie, welcome to Outdoorking. Thanks for starting out by posting pictures of your mower, so we all know what the subject is. I notice that your mower up to now has had a 2 stroke engine, of a type which I personally consider to be garbage, but of course there are others with different opinions, which helps make Outdoorking a diverse place. You haven't told us why you are considering changing from a, to put it politely, colloquial 2 stroke, to a global 4 stroke. While the 4 strokes have the advantage of running much better on much less fuel, they have the disadvantage of not being suitable for operating on extreme slopes. If you happen to need to operate on steep slopes, it might be better to consider a good 2 stroke instead of a bad one. There are several Japanese ones that are good quality.
If your objective is to convert your mower into a smoother, more economical, less smelly machine that doesn't eat spark plugs all the time, and has a carburetor that actually works reliably, either of the brands you named (Briggs, or Honda) can fulfill that mission easily. Essentially, if you are talking about a top of the line Honda (which means a pushrod OHV one) those engines provide the benefits more fulsomely but tend to cost quite a bit more. The oldest Hondas are side valve and only slightly better than Briggs engines, and the cheapest new Hondas are OHC and are designed for a short life during which they run almost as well as the OHV ones.
Unless you specifically want a new engine, you should be able to find a decent second-hand Briggs engine very cheaply indeed, but you will need to make some basic checks on its condition. Second-hand Hondas are less common, and more often than not have been run by a mowing contractor until signs of deterioration arose. I take it you are not interested in overhauling an engine, so you should probably only consider a Honda if you are able to verify its history and condition.
Bear in mind that your Powertorque engine uses a different blade boss and blade plate compared with a Briggs, so you would have to acquire those parts as well as an engine. You also currently have a snorkel-type air intake, and that would have to be adapted to fit a Briggs. On top of those considerations, Briggs engines commonly come with two different output shaft lengths, one of which suits Victa bases like yours, and the other fits Rovers and most other brands.
If you are looking for more information on all this, we will need to know more about your requirements and expectations from this project.
