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Not especially. The interest charged is a function of the outstanding balance and the interest rate only. If the rate is the same and you pay the same amount of cash per month, you end up in the same place.
Option 2 gives you flexibility if you want to pay less in future though of course.
NickCJ-
Also check any limits on overpayment, most mortgages tend to allow you to overpay 10% of the outstanding balance (not the initial principle) every year before there's any charge (and then it's typically 2%). This restriction usually expires when the fixed deal ends, which means you can negotiate a new fixed deal with them (or someone else) and pay off an unlimited chunk of money at this point too.
My latest 5 year fixed deal finishes next July, hopefully they'll contact me again 3 months early to offer me another deal at a lower rate (currently 2.89%).
Greenbank
Two options with the same mortgage (2 year fixed at 1.14%):
Select a term of 10 years, pay £1,200/month
Select a term of 20 years, pay £650/month and overpay up to the £1,200.
Why am I considering option 2? Because overpayments come off the capital, not a combination of interest and capital.
Would this make sense to do?