If you think rates are going to go up then fix as low as you can, but it's all ultimately a gamble. For example I have a reasonably good variable rate in UK of c.1.8% above base rate, but eventually the base rate will rise. But what to?
I could get a 5-yr fixed at c.3.5% at the moment, but rates would have to rise c.1.5% for that to be beneficial. If the base rate gradually went up to, say, 3% over the next 5 years then on my current deal i'd be paying 4.8% at the end of the 5 years, but over the course of the 5 years I'd have paid roughly the same as if going on the fixed now.
I was going to fix about 2 years ago when 5-yr fixed rates were slightly higher than they are now... and our base rate was actually cut since then, so not fixing back then should prove to have been a good choice.
So it just depends on where you think rates will go over the timeframe you're looking at, compared to the mortgage rates currently on offer.
If budgeting is your concern then fixing is better. If wanting to minimise overall payment then its a gamble, unless you have good insight into where rates will go and when.
Also, with mortgage rates as low as they are in the UK, paying off a mortgage early is not always the best way to maximise potential...
As said, my mortgage rate is c.2.1% at the moment, but a reasonable return from the stockmarket should easily exceed that (e.g. 5%, being conservative over the long term). So if I invest in the stockmarket rather than paying off the mortgage I'd be earning c.2.9% net on that amount.
If, however, your mortgage rates are higher than expected returns from investing then pay off the mortgage.