Got two bikes, one of them is more exhausting to ride, what can it be?
I can see 3 possible causes for the bike being more exhausting than it "should" be:

1: Lack of (or incorrect) previous maintenance.

Particularly you mention you bought it from a "clueless" person. It is likely that such person didn't knew when to take the bike to maintenance and was not very careful on how or where to keep it while not in use.

Some bikes are factory packed with such types of grease and lubricants that in short time can gum-up, and cause a seizure-like effect instead of reducing friction. This happens particularly in low end bikes, where cheap grease is used, so it lets evaporate part of the oils leaving only a paste-like residue. This may not be evident when moving parts by hand, but a tiny amount of resistance in every axle adds up when riding. When this happens in the pedals and bottom bracket, the effect on the rider is very noticeable, still the bike is felt to roll freely, but heavy to pedal. 

The fix for this is a complete disassembly of the hubs, bottom bracket and pedals, cleaning completely the internals and reassembly with good, fresh grease. Of course this covers correct re-adjusting of hub cones, bottom bracket cones and pedal axle, etc. which may be currently over-tightened.

The chain may also be suffering from this. You can change the chain or deep clean and re-lube it.

2: Low end components too low

Some bikes are produced with low quality components, which are not formed properly and are made out of incorrect materials. In particular, chainrings, bottom bracket and cogs. Low end ones are made of low grade steel which is heavy and kind of soft. The heavy part has an obvious effect. 

The softness of the steel is a major problem. When bearing cups or cones are made of soft steel, the balls "sink" into them because the steel flexes a bit, creating resistance. Think of it like rolling a pool ball on a bed, versus rolling it on a proper table (which would be a bearing on proper steel). This effect is very subtle and can not be noticed when moving parts by hand, but when real load is applied (i.e. actually pedalling) it is greatly increased. A similar thing happens between mild steel chainrings and the chain.

Also, poor quality components are often poorly machined, which means they do not have the right shape, just a very similar one.

This is the main difference among low end components and reputable ones: the quality of materials and machining used.

The only remedy for this is to upgrade components. It is not necessary to break the bank, there are a lot of good, affordable components made by reputable makers, which can be a good option. For example, almost any Shimano component from the basic line will perform better than a generic brand-less component from a Walmart bike.

If it was my bike and I needed to make it easier to ride, I would upgrade bottom bracket, crankset and pedals first followed by cog set and finally hubs. (And I would do it progressively, not all at once and only if the bike frame is worth the effort).

3: Geometry and fitting Issues
A bike with different geometry can be more tiring to use. Besides this, a poorly fit bike makes the rider-bike system less efficient. The bike may have good geometry but be severely far from a proper fir for the rider, it may even be the incorrect size.

Do a search for "bike fit" to check some critical points like saddle height, and effective top tube length, among others. If you can't adjust the bike to get it close to the recomended positions the bike may be too small/to large for the rider.

Other factors
I have left this apart because it is kind of obvious but:

Check if tires are properly inflated and in good shape. Tires at lower than recommended pressure generate more rolling resistance. A good tire can safely go up to the max pressure labelled on its side. If it doesn't seem to be able to hold up, then it may be too old and must be changed.

Check for rubbing brakes, or tire rubbing on frame.