Luxury Vinyl Tile (LVT) is available in many different varieties. Board rigidness is definitely a consideration when choosing an LVT. The tiles or planks are available in a soft flexible plank, semi-flexible plank, or rigid core plank. Typically, the expense of the LVT will increase with the rigidness of the plank you choose.
Thicker does not always mean better. The durability of the LVT should be measured in the wear layer, which is in mils. The board's rigidness can provide an easier installation. If you have a smooth, flat surface a thinner and flexible LVT with a higher mils wear layer would not be a bad choice.
The thinner LVT can show “telegraphing” of flooring imperfections. If the flooring has irregularities it would be wise to choose a rigid plank LVT to cover the underlying damage. If you have a thinner, flexible LVT imagining may show through with strong patterns or damaged areas.
A rigid board can help strengthen old subfloors. If the residence is very old and could have weaker subflooring, the rigid LVT would help distribute weight across the flooring and away from specific spots. The surface will still need to be level to ensure the board connections stay clicked together.
A flexible click LVT would be an excellent choice to float over an existing sheet vinyl flooring. The board thickness would be minimal, and the installation would not overly increase the flooring height for nice transition between flooring surfaces.