I don't really feel that there is a right or wrong choice between the 3 KW MEP-016D and the 5KW MEP-002a for emergency home backup assuming typical 3-4 day annual run times, etc. There are just advantages and disadvantages each way, this is of course assuming that 3KW is enough for your vital loads, and keeping in mind that the MEP-002a is going to have about double the real world potential power output. A lot comes down to how you plan to use and install it. Being fairly light the MEP-016D can be kept in a shed or garage and moved out when needed, the MEP-002a will either need a permanent outdoor home or modification to be portable (assuming you don't get a trailer mounted version of either). On a total cost of ownership point of view, the MEP-016D likely wins, with smaller oil sump, cheaper / smaller filters, and that all important ability to pull start and be jump started without need of having its own dedicated batteries. Sure bigger tends to be better with filters and oil, but there are those that say the Yanmar's don't need as much being a more modern engine, both in design and manufacture (I am not going to take a position on that one, other than they both seem to hold up in the field for thousands of hours). Note the military rebuild schedule on the MEP-002a is about twice as long as the MEP-016D (5,000 vs 2,500 hours I think, but your not likely to run into either one with home use any time soon).
Ike
p.s. on choice of military surplus 5KW generators, the practical choices are the good old MEP-002a and the new MEP-802a, of the two for now I would suggest the older MEP-002a, they tend to sell for less, but more importantly there are lots out there, and lots of members here to lean on for support, if you get a MEP-802a, you will have a much smaller pool of peers to lean on and parts can be hard to find even though they are newer as there are not that many in civilian hands yet.