You can think of FHE as just "you can compute arbitrary polynomials over ciphertexts". You can't exactly get conditional execution using polynomials. Most people instead think of FHE computation as "arithmetic circuits".

Also, some schemes offer extra stuff for free. BFV (https://eprint.iacr.org/2012/078) for example lets you compute Frobenius endomorphisms very cheaply. That is, given ciphertext c, you can compute c^q without having to do log(q) many squarings, where q is the characteristic of your ring.