They're all beautiful, each in their own way. Mostly, Le Puy probably has more ruggedness to its character than the others.
I should probably elaborate by means of comparison.
The Paris/Chartres/Orléans/Tours Way is characterised by the wide swathes of flatlands and fields and forests and gentle hills and agricultural beauty that it cuts through, which can be quite spectacular indeed in the vibrancy of colour and the clearness of light that can arise in those regions, whilst also being -- from a hiker's/pilgrim's perspective -- the easiest and the fastest of the major routes to the Pyrenees, the only seriously major geographical obstacle to take into account being the Gironde/Garonne river system. No O Cebreiros on that route, but quite a few 30K+ stretches of nothing but fields or forest 'til the next watering hole. Food is also very good, if a bit standard bourgeois French, and if you correct your course properly, the spiritual & religious aspects of that Way are quite meseta-like in their depth and purpose. Approaching, nearing, entering, then praying and sleeping at Chartres in particular is a matter of humble majesty.
The Vézelay is a kind of smorgasbord of all of the other French Ways -- its gentle and hillier sections from Burgundy through the northern foothills of the Massif Central are as the Tours Way, with perhaps more engaged hiking, but less opportunity for meditative spirituality. It's rockier sections are muted, not violent nor hateful towards your knees. Food, cheese, and wine also much better, obviously. But it has not the escarpments of the more southerly ways either, for even the passage through the Dordogne is more moving feast than daily hiking plan. It's the Way of choice for the more fleshy-minded among we pilgrims, who like something perhaps not too harsh, but challenging enough ; same distances and hiking, but all facilities and mod cons to get into it more gently and at leisure ; happy for all budgets from the el cheapo up to the full tourigrino 5-star package ; and you get to see Burgundy, the Loire valley, the fat Dordogne, down through the Gers, and more vineyards than stamp-places on the blankest of your
credenciales.
Le Puy I'll simply leave to the fine descriptions of others elsewhere.
The Arles is basically just the South of France route. Mediterranean diet, hills, valleys, mountains, plains, deserts, forests, fields, vineyards, villages, mountains, lakes, cities, superficial and cheeky southern French with a twinkle in their eye and a sing-song accent, the rougher southern wines and their equally silly cheeses and peasant fare, all lashed down with gallons of olive oil and dodgy apéritifs, dead serious involved discussions about the silliest and most frivolous matters, and no, they won't really give a fig that you're a pilgrim either, though they will also gladly give you figs galore to feed your belly with, and happily give you and your mad quest the best help they can give along the Way.
The Piedmont is fundamentally a more rural, more mountainous, more solitary, not necessarily more difficult (it's a lot rougher, but also much shorter), more Catholic, more solitary, less superficially friendly, cleaner-aired, often frustrating but equally often most pilgrim-like variant of the Arles. (it is the oldest of the Ways through France, as it is the traditional Camino from Navarra and beyond to Rome, older than the discovery of the Apostle's remains at Compostela) It has the beauty, particularly as you begin to approach Lourdes, of its gradual transition from pure hiking concerns towards the more spiritual, then religious, then Christian, then very powerfully Catholic as you reach Lourdes and walk beyond, a Pilgrimage in its full merits, and yet still within your pilgrimage on the Way of Saint James. Arles Way cheekiness also, but with a certain mountain-people's thoughtfulness perhaps not encountered elsewhere at length.
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But, all things being equal (which obviously they aren't), I'd still always recommend the Vézelay. It's as much North and South, material and spiritual, deeply beautiful and hikingly easier, and really is just a general combination of the qualities of the others.
But if you are looking for a less messy Camino, in whichever way, all the others are wonderful in their own purposes and beauties.
