What is the difference between wool and cotton Tzitzis?
Do they have the same Chiyuv?
Is there a Hiddur to wear wool?
What if one gets hot easily?
The difference is like this- according to all opinions a four cornered garment needs tzitzis min hatorah if it is made of wool or linen, regarding other fabrics it is controversial if it is min haotorah or not. The Rema O:CH 9-1 says that the halacha is that all garments are d’orayso, however numerous poskim say that a yirei shomayim should be stringent and wear a garment of wool because there are opinions that only wool is d’orayso. Additionally, there are opinions that we can only put woolen strings on to a woolen garment and not from other fabrics. Therefore according to numerous poskim it is preferable to wear a wool garment over a cotton one. This would also apply if one gets hot easily.
Mishna Berura 9-5, Gra”z 9-4, Kitzur Shulchan Aruch 9-12, Halichos Shlomo ( Teffilah) 3 ftnt. 25, see Igros Moshe O:CH 1-2 and O:CH 2-1 Y:D 3 52(3) that this the preferred thing to do and a baal nefesh should be machmir even if one is hot, however if one can’t manage it, it is permitted to wear wool strings even if the garment is a different material. The Chazon Ish was not makpid on this and wore a cotton garment, see Piskei Teshuvos 9 ftnt. 19.