Well, first off: you should not make that trade under any circumstances. Of course it depends on the condition of the card and such, but as far as average market price goes, a Rainbow Dragon is worth about ten Ultimate Tyrannos of equal condition. Trading it off would be a very, very poor deal indeed. Simply selling the card at your nearest card shop and buying a single copy of Ultimate Tyranno from there instead would probably leave you with a fair bit of leftover money in hand and thus already be the better deal.
As for your Dino/Beast dilemma. Well, if half your deck is dinosaurs already then obviously the crystal beasts are doing poorly. The Crystal Beast theme has some powerful combos and cards to its name, but it requires a highly focused deck that doesn't mind not using its spell and trap card zone for much else. They have basically zero synergy with dinosaurs, so I really have to wonder what you were thinking trying to combine the two in the first place. Also, attempting to play Rainbow Dragon outside of dedicated Crystal Beast in the first place is already extremely silly business.
Neither is uber-competitive right now, but still: Crystal Beasts played right are superior to dedicated dino by far. I'm going to go out on a limb here and say that the problem here is not the cards themselves but the deck as a whole.
SO, my suggestions in short would be: keep that dragon, and get yourself a playset of the good crystal beasts and their strong support cards. Sapphire Pegasus and Topaz Tiger are beasts you'll basically always want to max out on, and Rainbow Ruins, Crystal Promise, Crystal Blessing, Crystal Beacon, Crystal Release, Crystal Tree and Crystal Abundance are all strong cards in their own right that will most likely make your deck perform better. Rare Value used to be another given, though apparently it's not doing too hot nowadays.
But yeah, Crystal Beast > Dinosaur. Rainbow Dragon > Ultimate Tyranno.