frankly, i agree with your friend. this combo has never done me wrong, because it allows me to have a good chopper and a good fine cutter...
a single mid-size knife does neither spectacularly, but does both okay.
as far as pros of a single midsize or large fixed blade...well as said you only have to carry one tool, reducing weight (most weigh less than a hatchet alone, disregarding folders which are normally pretty light). this also means that you have only one tool to clean, sharpen, and otherwise watch after. you have fewer failure points, no pivot as on a folder, and a solid steel tang (assuming you are using a traditional wood handled hatchet as the argument). you have a knife that can be used to chop okay, and you have a knife that can be used to whittle roughly. all in one tool. you could also argue that you can attach a survival kit to a mid or large size knife, though it could be countered that you could do the same with a belt pouch or a hatchet sheath.
also, a fixed blade can be used like a mini machete, to hack at small vines or tall grasses that are in your way. if you try this with a very forward balancing hatchet, you are likely going to end up with a hatchet in your leg.
it is easy to baton firewood and smaller kindling with the fixed blade. on the other hand, one of the primary uses of the hatchet is that purpose, without the need for a baton. what's that? you say you can't use a thick bladed hatchet for splitting that really little matchstick kindling you need to get the fire going? you are either using an improperly ground hatchet, made for chopping cement, or you don't know what you are doing. on the other hand, it is admittedly difficult to split the really small stuff with a hatchet. this is when i carefully use my folder (most often an opinel these days) with the lock disengaged, to split the pencils down to toothpicks. it works well.
basically, you could talk for a million years about this and still never come to a definite conclusion. ultimately it is based on personal preference. if you grew up with a machete or other mid or large sized fixed blade, or lusting after one, you are likely going to be most comfortable with that tool, and know how to use it to maximize its strong points. on the other hand, if you grew up with a hatchet on your belt and a folder in your pocket, you are going to know how to best employ this combo to maximize the benefits.
it would not shock me if two men, with all other factors equal, were put side by side and each given one of the tools or tool sets as the case may be, and were told to do exactly the same tasks, they would most likely do them equally effectively, employing different means to reach a common end.
