I'm running a 5 speed 'box with my 1600 (stock except twin carbs).
Runs 3500 rpm at 70mph - much better than the standard 4th gear
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Conversion can be done for similar money to a decent 6 rib (4 speed 2L late bay) gearbox too.
The biggest upside is having a 5th gear means you've got smaller gaps between the gears, better for acceleration and hills
There are a couple of downsides:
The first is that gears 1 and 2 are a bit tall for a 1600, meaning low speed acceleration is possibly a little slower (than the 1600 gearbox), particularly uphill. Gears 3-5 are perfectly placed. I'm sure with a 1776+ it'd be fine - I've probably only got 55hp to play with.
The second is that the Porsche 901 gearbox has older style synchros (when compared to the stock gearbox), meaning that a slightly relaxed gear-change lever speed is beneficial for the synchros to do their thing. Not a problem unless you're racing, I'm not sure most people would even notice