Just a few points...
Regarding payload- 40mm HV (H&K GMG/Mk 19) Average around 30-40 grams of HE. 60mm- 300 grams
Weights- 40mm, belt of 36 around 20-30 kg (this is off the top of my head from working with Marines are few years ago). 60mm- 4 pack around 10 kg (81mm comes in the three packs btw Capt Sensible).
So weight for payload is around the same, just delivered in a different number of rounds.
Range of the H&K GMG is 2400 metres max, 2000 effective. 60mm out ranges it, but only in bipod role. Handheld, I seem to recall you can only fire it at Charges 0/1/2, this may have changed.
So, neither are packable if you want any sustained fire. So assuming you have a vehicle to truck around the ammo what are the pros and cons.
60mm pros- More HE per round, better effect on buildings, esp if you fire on delay. Longer max range. More versitile ammo (HE/Smk/etc). You can pack it with a couple of rounds.
60mm cons- Weight of fire not as good for "shock effect". Slower in the direct fire mode and using ammo to adjust eats up what ammo you do have quickly. Not that good against armour.
40mm pros- Heavy weight of fire. Better suppression. Some (not much) effect against armour.
40mm cons- Packable in the same way a .50 cal is packable (not very). Shorter range. Illum and smoke (if available) is not as useful as the 60mm version.
There are some very nice airbursting rounds that use prox fuzing are are can maximize the beaten zone that a is produced rather than sending most of the frag up. Where these are with regard to in-service suitability I dont know, but the ones I saw were "in development" 18 months ago. In my experience that means, we've designed, they've worked a couple of times, if some government wants to throw money at us we'll actually get them working reliably...sometime.
The RM are still putting the 51mm to good use along with the 40mm HK GMG. Different courses for different horses, isn't that how it goes?