In the title you said "Tift", but in the body of your question it says "tight". I assume you mean "Tifton"? If so, that's a type of Bermuda grass, which has relatively small stems and narrow leaves, so it shouldn't look like straw.
As with any hay, the nutritional value will depend on many factors, like the amount of growth when it was cut, and what (if any) fertilizer was applied to the soil.
I don't know anything about peanut hay, or why your cows would prefer it. Maybe the new hay is poor quality, or maybe your cows just aren't accustomed to it, or maybe the peanut hay is just more palatable than the Tifton (if that's what you have).
I haven't fed it in years, but I've never seen a cow turn down peanut hay for anything else. Once they get used to something, they'll eat it more readily than anything new you put out there. I bought some really good Jiggs hay one year and started feeding it halfway thru the winter after I used the last year's Pensacola bahia. They turned their noses up at the Jiggs and went back to the remains of the bahia for about 3 days.
If it's tif 85 and barn stored it should be brite like straw but that's where the comparison ends. They will not touch anything else if pnut hay is there. The 85 is good hay if it was cut right and shouldn't need any supplement. Mine will eat the Bahia first then eat the 85 if I set the rolls out for them to choose. I do that this time of the yr when grass is trying to grow some. Around here a good roll of 85 will fetch 40 to 50 bucks a roll from the horse nuts.