Hi Lauren,
OK, the only difference is that you will pay peak rates in the evening that way round. So for Shoreditch that would be 2x £5.70 = £11.40. For Old Street you’d cap at £13.10 regardless of whether you changed at Vauxhall or Waterloo. I think the quickest way across London on the tube is likely to be Waterloo and City between Waterloo and Bank followed by Northern line to Old Street.
Sorry for being confused by your journey description.