When people compare two wooden tables they usually compare the timber, and the timber is rarely what they end up living with. The finish is what your hand touches, what spills land on, what scratches, what dulls, and what determines whether a mark can be rubbed out in ten minutes or requires the whole top to be stripped. It is worth understanding the four common families.
Oil finishes soak into the wood rather than forming a film on top of it. Because the finish is in the surface, the surface still feels like wood, the grain is clearly visible, and the colour deepens slightly. Oil offers the least resistance to water rings and heat of the film finishes, but it has an advantage nothing else matches: it repairs in place. A scratch or a dull patch is sanded lightly, re-oiled and left, and the repair blends because there is no film edge to feather. The cost of that is maintenance, usually a wipe of fresh oil once or twice a year on surfaces in constant use.
Wax sits somewhere between a treatment and a finish. It gives a soft, low sheen that many people associate with old furniture, it is very pleasant to touch, and it is trivially easy to renew with a cloth. It offers the least protection of anything here and will mark from water and from anything hot. Wax over oil is a common and sensible combination on pieces that are looked at more than they are used. Wax alone on a kitchen table is optimistic.
Lacquer forms a thin hard film on the surface. It is what most factory-finished furniture wears, because it sprays quickly, dries fast and gives a very even result. It resists water and daily handling well, and it is the finish most likely to still look untouched after five years of moderate use. Its weakness is repair: a deep scratch goes through the film, and because the film is thin and uniform, spot repairs show. Damaged lacquer generally means refinishing the whole surface.
Varnish is the toughest of the four and the most obviously present. It builds a thicker film, stands up to water, heat and abrasion better than anything else in common domestic use, and is the usual choice for floors and for table tops that will be treated badly. The price is appearance and repairability. A heavy varnish puts a visible layer between you and the grain, and when it eventually wears through in traffic lanes the only real answer is to strip and start again.
Choosing between them is mostly a question of how the piece is used and how you feel about marks. A surface that will be used daily by a household that would rather not think about it wants lacquer or varnish. A surface that someone is willing to maintain and would rather see age wants oil. A piece that is mainly decorative can take wax and will look better for it.
Two practical notes. First, finishes do not layer freely: oil and wax can generally go over one another, but nothing sticks reliably to an old waxed surface, so a piece that has been waxed for years has to be cleaned back before it can take anything else. Second, identify the existing finish before you attempt any repair. A drop of water left for a minute will raise a mark on wax and oil and sit harmlessly on lacquer and varnish, and a few strokes of fine wire wool in an inconspicuous place will tell you whether you are cutting into a film or into the wood itself.