Thats the way I see it:
Gentailers ... are basically quasi bonds. Their dividends have little to do with the price of real estate, but lots with the interest rates bonds are paying. If interest rates go up stock prices need to go down to make sure the dividend return is comparable to the interest rates of a bond.
Rising interest rates are bad (if you own Gen tailer shares).
REITS are similar but come with a double whammy related to interest rate rises. Obviously - the quasi bond relationship works as well as for the Gentailers above, but on top of that do you have the impact on their NTA. Rising interest rates means that it is more difficult and expensive for purchasers to get loans which ultimately will bring property prices down, which has obviously a negative impact on NTA.
Rising interest rates are really bad for REITS. Obviously - they won't kill them, but they bring the share prices down.