Emerald can carry much more weapons... and cheaper...

The Emerald is an AA ship like the Emden, Omaha etc, but can be a pretty effective for ship-to-ship combat thanks to it being able to mount pretty powerful guns (RN dual 5.25 and dual 6 inch).

The Dido is a very powerful anti ship CL, you could say its overpowered for a ship of its class. It can mount more armour than CLs and even some CAs of other nations with the right setup, allowing to deflect shells up to 6inches. Its also very small for cruiser, making it even more harder to hit.

The emerald can mount more guns than the Dido but it is a much bigger target and the gun placements give it a pretty wide spread, whilst the dido can mount a lot of armour, is very small and can focus all of its guns in a tighter pattern.

Emerald. Hands down.

Both ships have R slot sizes in the low 80s' (84 emerald, 81 dido) and the same fire control, and thus mount the 5.25 rp10 guns or dual 6" guns as their primary choice with equal accuracy. And both mount 9 crew total (5 above, 4 support).

But Emerald has a 6 turret broadside (5 center line turrets, 2 wing turrets), Dido has 4. Emerald also has better firing arcs and a significantly higher turning force (27 as opposed to the 22 on the Dido). This means the emerald has more firepower and can more easily bring it to bear. And with space for 1 more bind of ammo, it can keep firing that much longer.

Emerald also has 4 T slots to the Dido's 2, and can mount a scout plane.

Emerald all the way. Its is effective with AA and HE shells. I managed to take out a dunk in an emerald once :-). But that is at higher levels. Emerald have brilliant broadside damage in blitz due to number of guns. I think I may have tried the dido once and never used it again. The remodel of the dido (sirius) can go epic AW in blitz if I remember correctly, but even so it will slow you down and the guns you mount arent, IMO, as effective as those mounted on the emerald.
In conclusion, my advice is to stick with the emerald until either the york or the edinburgh, Better damage and same/ similar range.

Emerald if you like to have lots of guns (at the sacrifice of how much you can AW on it). it's also one of the better UK ships for AA play if you go into GB games with it, with it's 7x R slots.

the downside of the Emerald, outside of it's lack of ability to take much heavy punishment, is if you're using Auto FCS, instead of the manual Aiming FCS, you'll almost always having 1 or 2 guns going wonky on you, and you be constantly at risk of friendly fire as they shoot off in oddball directions but the one the rest of your guns are shooting at (and causing you an exp penalty along with it. and probably some insults from players who'll think you're a noob for shooting at them *shrugs*)

the Dido, you can go heavy AW on it, it's slower than the Emerald even with normal .2 deck & .2 belt, with some bulge & bulkhead added in for protection but not overdoing it.

on the other hand, you get 4x R slots, and can pack quite the punch with the 6" duals, or even the 5.25" MK II duals.

the Dido, at level 34 I believe, you can remodel into the Sirius, which gives you a 5th R slot for added punch. quite a number of people take the Sirius Remodel, go front turrets only, then AW it to the max. as you've probably run against a few times.

downside of the Dido/Sirius? it's speed, and that's not even counting if you go full out AW with it. but the armour & damage dealt do make up for the difference if you play her smart.

in the end, it depends on your playing style, and what you want to use her for. or how well you can adapt coming out of a much faster Destroyer ship.