When you lower the traveler, the shape of the main is maintained. If instead you ease the main-sheet, the shape of the main changes quite a bit because you are not only letting the boom out but the back end of the boom rises. When the boom rises, the leech (trailing edge) of the main to opens inducing what is called twist. The leach at the top of the main becomes much more open than the leach towards the bottom of the sail. If you want twist, great. If not, Doe!
Say you are sailing directly to your desired destination. You worked hard and finally got all the tell-tales from the top to the bottom streaming back on the main. The wind shifts ten degrees towards the back of the boat causing the tell-tales to curl around to the back of the sail. Just ease the traveler until the tell-tales are again pointing back. If you instead ease the main-sheet, you cause twist allowing the top part of the main to open further than the lower part. You will notice that the top tell-tales recover but the lower ones are still curling around the back.
If you continue to ease the main-sheet until the lowest tell-tale streams, the top tell-tales will not be streaming. You might use this "excessive" twist setting when sailing in wavy conditions. As the boat weaves its way through the swells, some part of the main sail will be providing drive. As the boat turns away from the wind, the top tell-tale is streaming. As the boat turns towards the wind the lower tell-tales will be flowing.
If you sail on a boat that has a boom-vang, but no traveler (or you decide not to use the traveler), you can use it to prevent the boom from rising when you ease the main-sheet. I think they call this technique "vang sheeting".
When the traveler is positioned directly below the boom, the primary effect of easing or tightening the main-sheet is that the boom rises or lowers. When the boom is all the way out, say perpendicular to the boat, the effect of easing or tightening the main-sheet is that the boom moves out or in. As the boom comes in, the effect of the main-sheet the transition from "in and out" to "up and down".
When sailing down wind with the boom all the way out, tighten the boom-vang to reduce some of the twist of the main.
As you learn more and more about the various control lines, you find that each usually has a primary effect and many side effects.
Why might easing the traveler be better then easing the main-sheet? If you boat does not have a back-stay, you may be depowering your main but you will also be powering up your jib (if you have one) and in certain respects, also may be powering up your main. The back stay goes from the top of your mast to the back end of your boat. When it is tightened, it removes power-inducing sag from the forestay. Also, it compresses the mast causing the mast to bow forward which helps to depower by flattening the main. Boom-vang pressure will also bend the mast.
Not only does positioning the traveler under the boom allow for the boom to lower when the main-sheet is tightened, but it also bends the mast and tightens the forestay.
If you have no backstay or boom-vang applied when you ease the mainsheet, the main and the jib get a more powerful shape. If you lower the traveler instead, you maintain the mast-bending pressure and forestay tension.
Also, by limiting the twist of the main by lowering the traveler, I think you also maintain a larger slot between the trailing edge of the jib and the front backside of the main. If you just ease the main-sheet, the slot may be more restricted.