Aldi closed their local branch here, so I tend to get to Lidl far more often.
However, once I'm in an Aldi or Lidl store I struggle (in general) to see any real differences. They stock similar products (probably sourced from the same manufacturers), at similar prices. Even their store layouts are the same. (I was in the Ipswich Aldi the other day and I knew where to find everything because their store is almost identical to the Stowmarket Lidl).
The only major factor which draws me to Lidl (other than simple geography) is their Super Weekend deals which, most weeks, include decent quality wine at really low prices. For example, their Bordeaux Superieur is a damned good wine for £4.99 (which could cost £8.99 elsewhere). However, for those who get there early enough, it's on offer at just £2.99 this weekend. Aldi also have good wines but I've yet to see them match offers like that one.