Is Je t'aime or Je t'adore the romantic phrase?

It depends. To whom are you speaking and in what context?
If you say "Je t'aime" / "Je t'adore" (I love you / I adore you) to a relative or good friend, it's not romantic at all.
Example: If my best friend surprised me with concert tickets, I'd say: "Wow, you're the best! I adore you! Thanks so much", etc. (No romantic tone, there.)
If you say it to your spouse or boyfriend/girlfriend, then yes, the phrases are romantic.

Hope this helps. =)