What extra gain is there? What extra work is involved?

Improved cases are no more work than a standard, as far as reloading and shooting, dies cost more. Brass lasts forever. With out looking at my reference material you should get about an 8% powder increase. That boosts your velocity up about 8%. Usually works out to 150-200fps extra with most Ackley's.

I just finished (less bluing) a 6.5X55 on a VZ-24 action and I too am looking at stepping it up a little.....which means I'm going to order a 6.5-06 reamer from Dave Manson.

As for improvement of a 6.5 improved I'd look at loading data for the .257 Roberts and the .257 Roberts improved.

My Hornady handbook (5TH edition) shows that there's no gain (barrel lengths corrected at 50'/sec per inch) in improving the case capacity. This is not what some will tell you but this is data taken from a pressure barrel and not someone's "wow look at that flat primer" load indicator.

If you have an action capable of handling the longer case I'd strongly recommend you look to the 6.5-06 but the 6.5X55 is a fine cartridge as-is.

My playing with it showed no real gains at all. The 6.5 bullets are very aerodynamically efficient.

That is why cases with larger capacity that the 6.5 x 55 or 6.5 x 57 start burning out barrels at a much faster rate.
Ackley's book with the chapter on bore capacity would make a little good reading.

Instead of going to 6.5 /06, I'd suggest looking at a 6.5 Rem Mag or a 6.5 Win Short Mag. My reasons are that their is great advantage in 6.5 calibers to seat the bullet out long in the magazine to maximize case capacity and it also adds to the bores accuracy capabilities. That is why the 6.5 x 284 is so popular, and it is also a much better choice over the 6.5 /06 or 264 Mag in my experience.

Good luck with it, YOU were smart enough to pick a great bore size to start with so you are on a roll!

Cheers and good shooting
seafire