The North would likely be better off today without the continuing reactionary influence of the South. The South would be a banana republic.
Good luck having the middle of the US thrive economically with Confederate control of New Orleans preventing importing/exporting using the Mississippi River. Loss of control of the Mississippi River Delta has staggering economic and political ramifications.
1861 is not 1803. The Chicago and Erie Canals and extensive railroad development would make the North quite able to manage its exports. Not to mention it's very unlikely the South would totally block Northern access to the Mississippi, given river tolls from Northern industry would likely be one of the few reliable sources of income many of those regions would have.
