Bikes designed for drop bars have shorter top tubes than bikes designed for flat bars. You will be in an even more upright position. You can compensate some by using a longer stem unless of course you like the new position. I have done this conversion multiple times and I like it.
Some will argue that you lose multiple hand positions but I have always felt this point is overrated. I do fine with just flat bars and my hands don't suffer. YMMV. You can always add bar ends for more hand positions.
The beauty is if you don't like it you can always change it back.