By the numbers, Solar Beam is more worth keeping for Ho-Oh than Shadow Ball is for Mewtwo.
Solar Beam - Power = 180
Fire Blast - Power = 140 + STAB (28) = 168
Both are good, strong attacks. Solar Beam does a bit more base damage (12 power), even after STAB. Now, here's where they differ.
Solar Beam is strong against Rock, Ground, and Water. Three important attack types. Solar Beam is weak against Fire, Grass, Poison, Bug, Dragon, Steel, Flying. That's also a lot, many of which are very important in the meta. And doubles like Dragonite and Salamence (Dragon Flying), Scyther (Bug Flying) and Crobat (Poison Flying) doubly resist Solar Beam. That means that the base damage against Scyther is 90, while the base damage against Golem is 360. Huge swing.
Fire Blast is strong against Grass, Ice, Bug, and Steel, and Weak against Fire, Water, Rock, and Dragon.
Bottom line, IMO neither is better or worse. They are different. I'd prefer to have one (or more) of each. Additionally, Extrasensory and Brave Bird is probably the weakest combination, but will be very effective against Machamp and other Fight types.
So I'd definitely hold off on the TM, especially since Gen3 is imminent, and if a new (or old) mon gets a killer move, everyone will have to use TMs for those. You can always TM the move later if you decide Solar Beam isn't useful for you.