Indiana University Sheet Music Collections has the sheet music. The most significant difference is the repetition of the last line of each verse. I have boldfaced the other differences.

WILL YOU LOVE ME WHEN I'M OLD?
J. Ford
Philadelphia: F.A. North & Co., 1872.

1. I would ask of you, my darling, a question soft and low
That gives me many a heartache as the moments come and go.
Your love I know is truthful, but the truest love grows cold.
It is this that I would ask you: Will you love me when I'm old?
It is this that I would ask you: Will you love me when I'm old?

CHORUS: Life's morn will soon be waning, and its evening bells be tolled,
But my heart will know no sadness if you'll love me when I'm old.

2. Down the stream of time together we are sailing side by side,
Hoping some bright day to anchor, safe beyond the surging tide.
Today our sky is cloudless, but the night may clouds unfold,
And its storms may gather 'round us. Will you love me when I'm old?
And its storms may gather 'round us. Will you love me when I'm old?

3. When my hair shall shame the snowdrift, and mine eyes shall dimmer grow,
I would lean upon some loved one in the valley as I go.
I would claim of you a promise worth to me a world of gold.
It is only this, my darling: that you'll love me when I'm old.
It is only this, my darling: that you'll love me when I'm old.