I'd like to recreate this "increasing size text" in Illustrator or Photoshop.
Which software should is better to use? What tool is the best?
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One a fast answer could be "apply perspective!". But that's not the same. Horizontal dimensions have stayed intact, the stretching is vertical. Perspective affects all dimensions.
In Illustrator you can get the right result with Effect > Distort & Transform > Free Distort:
In the Free Distort dialog simply drag the right side corners vertically.
If you watch carefully you see that the tilted parts of N and A (=less) have got some extra twists. Original letter shapes have little knees at the tilted parts. They have become more visible. It can be avoided by using another font or by removing the intermediate nodes. For it the text must be outlined (=Type > Create Outlines) before distorting it.
The extra nodes can be removed with Delete Anchor -tool which is under the pen in Illustrator's tool palette. It's tried here:
Free Distort is a non-destructive effect. You can remove or tweak it via the Appearance panel. By applying Object > Expand Appearance you can fix the effect for other edits.
This can be done also in Photoshop, but it has a drawback: If the tilted parts of the letters have some knees, they get amplified like in Illustrator. They cannot be straightened beforehand with path tools because there's no such editability in Photoshop.
The right distortion can be got with effect Warp Text. The right warping style is Arc with 0% bend + some horizontal distortion.
Normal Edit > Transform > Distort nor > Warp do not work with text, the text must be rasterized for them. Rasterized text loses sharpness, so use Warp Text.
Warp Text is available when you right click the text in the layers panel. Check in the Character panel that the text is plain without engineer-style attributes such as faux-bold. They would prevent the warping.
Finally you must stretch the warped text vertically. See the result after Arc 0% bend + 80% horizontal distortion and generous vertical stretching:
Alternate answer: In Adobe Illustrator, you could use envelope distort and leave the text fully editable:
The red trapezoid is on top - with a multiply transparency blend mode to make visibility easier: with the text and the trapezoid both selected, go to Menu>Object>Envelope Distort>Make with Top Object - like so:
This gives us this result, which looks a lot like your example:
But the nice thing is that the text is still live-editable as text, not having to be blown to outlines - so for my money, the easiest approach to get you what you need.