"Yes, that is a difficult "
"Yes, that is a difficult "general" question. So if you don't mind me "running on a bit" I will give you my opinion.
Since you currently own an outboard (your bio) I will assume you are looking for a replacement outboard.
When trying to determine the "cheapest" motor to run over a period of say 20 years that can depend on a number of factors.
IF you can do all the maintenance and repairs yourself that will significantly change the answer.
So where to start?
Outside of the US there is still some availability of NEW 2 stroke models (carb or efi). So for the purpose of my rambling I will compare the 90 horse Merc - available in 2 stroke (carb), 2 stroke DFI (Optimax) and 4 stroke models.
The "going" price for each is - 4 stroke $8300, Opti $8000, 2 stroke $6500.
So just in intial cost either the 4 stroke or the Opti will cost you an average of 75-90 dollars more a year than the 2 stroke.
Gas mileage - despite all the hype about fuel economy, actual "on water" tests show that a 90 4 stroke and the 90 Opti actually don't get any better gas mileage than the "old" 2 stroke.
It probably has something to do with the fact that those models are 25-30 percent heavier than a "classic 90".
The old rule of thumb still prevails - at wide open throttle expect the motor to burn about 10% of it's horsepower in gallons - so a 90 horse will generally burn 9 gallons per hour wide open and about 40% of that at cruise (the exact speed is different for every motor).
So, in general, no significant cost difference for gas despite what the mfgs would have you believe ((my source for tests is boattest.com who strap motors on, load up some test gear and take them out for a spin - check out the website for lot's of free info))
But you also need oil (an expense) to varying degrees.
In a single season with say 200 hours of run time on the water, if all were run burning say 7 gallons per hour average (just so we can get some numbers) the 4 stroke would be the big cost winner with 1 oil change (maybe 20 bucks for a decent synthetic oil).
The Opti would use 4-6 gallons of oil (it's mix is computer controlled usually in the range of 200-300:1 mix). But DFI oil is expensive, often retailing at $30 or more per gallon - so your oil bill could approach $200.
The convenional 2 stroke would use about 28 gallons of oil at a retail cost of about $12 a gallon (for normal "dino-oil") for a total cost of $336/year (for my fictional example).
Maintenance costs - all will need filters, impellers, thermostats, prep for storage etc, so the "common" maint items will generally be similar.
Both the 4 stroke and the DFI's on the market are computer driven (although there are some carb model 4 strokes out there at least for now - there is rumblings that the EPA will mandate that they will have to become "injected". This will effect the designs worldwide since the US tends to drive the market), multi-sensor motors and anytime you have sensors you are going to have failures.
Unfortunately, both styles have only really been in the wider market for about 10 years now so there is not any real (long term data) to show how they hold up, but even in the past ten years the failure rate of certain sensors can be considered "expected" in models less than 10 years old - and most sensors are expensive (200 plus dollars each).
A 2 stroke trouble-shooting scenario usually only requires a screwdriver and a multi or ohm meter. The ECU jobbies require a diagnostic terminal which usually means a trip to a dealer (and an hours labour) even just to figure out what is wrong in the first place.
Hey, you saved possibly upwards of 300 dollars in oil with a 4 stroke, you can now spend half of that at the dealer to figure out which 250 dollar sensor is shot
Are you starting to see a theme here?
The parts for a 2 stroke are often cheaper than the more "hi-tech" designs. Not because they don't break, but a carb gasket and some cleaner is far cheaper than a fuel injector.
Likewise, a 4 stroke has over 200 parts in the powerhead (even when you strip off the ignition etc). A conventional and DFI 2 stroke don't have valves, cams, rockers or springs etc.
If the part isn't there it can't fail.
I have probably raised more questions for you than you had in the first place.
So my advice is, go with whatever you are comfortable with, because in the end the cost is going to even out regardless of what you choose.
If your current motor is just "tired" why not consider an overhaul. Generally for about 2500 bucks you can restore an outboard to "like new" status and get possibly 20 years of added life out of it.
I am just finishing up a rebuild on my 25 year old 140 Evinrude and expect to get another 20 years out of it now.
Considering a replacement (Opti or ETEC) comes in the 12-14K range, even if all the hype about better economy is true, the next 10 to 12 thousand dollars in operating costs that I spend on my current rig is just "left over cash" from not opting for a new motor
My personal picks -
4 stroke - nothing but a Honda (even though they are the most expensive of the bunch - they are just plain better built)
DFI - either a Merc Optimax or Tohatsu TLDI - both use low pressure direct inject systems that I suspect will hold up better over the longer term compared to the extreme high pressure systems used by Yamaha and Evinrude
2 stroke - either Merc or Yamaha - both have a limited selection still available and most of the Merc line was (at one point) either built by Yamaha or they supplied the parts - making the two motors fairly equal in performance and reliability."