Sometimes. While new player bonuses vary wildly between online casinos, brand-new casinos entering a new market usually prepare something quite special in order to attract attention and compete with larger, already-established online casinos that may have larger game collections or more word-of-mouth recommendations from fellow players. As the new player bonus is generally the biggest bonus a player will receive, it could be fair to say that the bonus at a new casino will have a bigger value than the regular promos at your current casino.