Alright... I've quickly made a army list and checked if i could fix the Royal in it or not.

Warband 1:
Theoden, armoured horse, heave armour and shield
5 Rohan Royal Guard with horses and throwing spears
5 Riders of Rohan
Warband 2:
Theodred, horse and shield
10 RoR
Warband 3:
Eomer, horse, shield
10 Ror

or...
swap Theodred for Gamling with the Royal banner and Meriadoc with pony and shield and swap Eomer for a captain with horse, heavy armour and shield.

Exactly the same amount of points, but a big change of abusing the Royal Banner with Meriadoc and calling heroic movements every turn...

What would you do if it's for a regular game with a friend or if it's for competitive play?

I have played quite some games against rohan with the new rules and I'd see the above list is fine for regular play.

For competitive play I would pick Theoden and Gamling.
In the new edition gamling also effects himself with his banner. In previous editions (one ring rulebook and kingdoms of men sourcebook) the royal standard stated: ... this does not include Gamling himself. But in the new edition, this is no longer the case.
In my opinion, both thedoen and gamling are now a auto-include for any competitive rohan army combined with as many royal guard (fight 5 on charge) as possible or RoH with throwing spears.
However, I noticed that such a aggresive army is weak to combat heroes using heroic combat to get to your heroes. At 750 pts I would add eomer as he gives you an answer to enemy combat heroes.
Besides, another neat little bonus of the theoden gamling combo is that gamling has sworn protector Theoden, meaning that on the first turn your army breaks both theoden (last stand special rule) and gamling will automatically pass their courage tests, making it very hard for your army to run away (especially if a lot of them are royal guard).