You should never give your girlfriend an engagement ring you bought for your ex-fiancé.
1. You picked and or made this ring thinking of your ex... Therefore it symbolizes the specific connection you had with her.
2. It is simply tacky
3. It's stingy... the actual cost in the ring is in the diamonds or gem stones the cost of the gold is hardly worth the indecency.
Women are usually more emotional and sentimental about the meaning and symbolism behind an engagement ring. It is more likely that a man is to think "Well why would I buy her a new one when I have this old one sitting around?"
Keeping the stones especially if they are heirlooms is reasonable and most women would not have a problem with this.
The difference is the stones were made long before the ring was even thought of and a woman of good character and judgment would understand the importance of keeping a Grandmothers or Greater stones around.
For goodness sake you can trade in the gold mounting for its gold value...spend an extra few hundred dollars to buy her a new mounting and put the stones back in the new ring. If you are really concerned lock the item away in a memory box or sell it on eBay. Then buy her a whole new ring with stones. If you spent the money to do it on the ex what is so bad about doing the same thing for the woman you want to spend the rest of your life with? Though I mention money it is only because this is the common issue I hear about. It is mainly about the principle behind giving a new fiance your ex's ring.
Most women would be insulted if they found out you gave them a ring you had bought for someone else in the past.