First of all, if you want to achieve confidentiality you should always encrypt with the public key, not the private key. RSA encryption is not defined for encryption with the private key, and the results may vary (especially the kind of padding that is applied).
For direct RSA encryption, the size of the encrypted message is identical to the modulus. Now the modulus should be at least 2048 bits by now, and your message is only about (27/3)*10=90 bits. So RSA would have a large overhead, independent on the key used. Using ECIES is therefore likely to give significant benefits.