Do ESP 7 string guitars have a longer scale length than 6 string equivalents?

ESP tend to use 25'5" scale lengths for their 7 string guitars. This is a very normal measurement for both 6 and 7 string guitars but it is worth noting that guitars such as the Eclipse models, which normally have a 24.75" scale length, have a 25.5" scale when made as 7 string instruments.

What is the difference between an ESP 7 string model and an LTD 7 string model?

The main difference is country of manufacture. ESP guitars are made in Japan whereas LTD models are made in Indonesia and Korea. There is more to it than just that, though. ESP guitars have a higher level of workmanship and the hardware used is often of a higher quality.