What's ideal size for a listening room?

A room with these ratios is ideal:

Height - 1m

Width - 1.618m

Length - 2.618m

Extrapolate that to your room and the bigger room is best for. Also a larger room means the room modes are more spread out which makes room treatment less of a pain.

I'd go with the 15' x 20' with 8' ceiling room. While its dimensions don't perfectly align with the Golden Ratio, its larger size and higher ceiling will provide a much better starting point for achieving good sound, especially when combined with proper acoustic treatment (bass traps, absorption panels, diffusers) and careful placement of your speakers and listening position. @emergingsoul 

Both rooms have excellent dimensions. I like the larger one because of the 8 ft ceiling. It will take more power to fill it up. It will give you more room for speaker placement on the short wall which is optimum in a rectangle room. When you say it is more open, ideally in the back would be best. Open on either side would be difficult to deal with acoustically. Nice you have options. Have fun with it.

14' x 20' x 8' or some multiple thereof.

Curious as to what equipment will be used?

@emergingsoul   I don't where anyone gets their information as to what room dimensions work best, here is a rather long article that explains the theory behind one calculator that shows how any combination of L x W x H of a room will affect  your the best possible sound.  This is only a start as acoustic treatments will play an important role in any great sounding room.  The whole story is here:

https://digistar.cl/Forum/viewtopic.php?t=557

If you just want to jump straight to the calculator, it's here.  The idea is to have the little dot end up in any area that is Black (best) Grey (good) and white (avoid). 

https://www.acoustic.ua/forms/rr.en.html

The findings of this calculator are proven when the same numbers are entered into other accepted programs.  I believe this calculator simply fine tunes the results.  This calculator does not agree with some of the suggestions already given.  I'm not one to say who is right, but it's an interesting read.  IMHO.  Cheers.

Here is another good calculator. https://www.hunecke.de/en/calculators/room-eigenmodes.html

Basically it is whatever room the wife will allow me.

It should have a door that closes and locks.

Would either of the rooms have any kind of sound treatments? 

This question is too generic for any kind of specific answer(s).  For example, first and foremost, what type of sound system is being used?  Are the rooms in question strictly rectangular or do they have odd kitty-corners or odd shapes?   Doors, arches or other openings?  Acoustical properties (e.g.  Typical drywall construction?  Insulation?  Solid cement, wood or other type walls & ceilings?  Windows?  Curtains?  Drapes?  Etc.)?  All of these are factors.

If it's not too much of a PAIN, set up your rig in both and let your ears tell you which is best.  Generally, my guess is the room with the higher ceiling would be your best bet.

@emergingsoul   You mention that the larger room is "open."  If it is open on one long wall and not the other (as is my listening room), you’re apt to get the best results with panel speakers--they lessen side reflections, compared to box speakers.  If you have a full, hard corner for just one speaker, the bass will be stronger on that side, and this is worse with box speakers.  Luckily, some panel speakers bring other benefits--their taller height can allow for better vertical imaging, and they are good at creating soundstage depth.

A larger room is likely to be better at handling louder volume.  So if you want to listen at realistic volumes to rock or orchestral music, the larger the room, the better.

Larger and more open sounds like the better choice. "Filling" is a very mixed bag. The smaller the room the more problems are reflections. I have a big Z shaped room(s). about 35 by 40. It is ideal. There are hall ways and asymmetries everywhere. My dealer says it is the very best room he has heard save one, and he has heard hundreds... many purpose built. The room itself... a leg of the Z is 25' by 20'. I have not trouble filling it... because I have a 9' triangle listening area with the back wall being about 4' back from the speakers. No reflections from the rear and none from the side. It sounds great. 

Go for the bigger room unless it prevents you from turning it up to what ever volume you want because it will disturb someone. This is more important. Any room with enough work can become great. 

The 8’ ceiling for the win every time.

It's a stadium there i said it.has my favorite bands playing some of which are dead. Enjoy the music and find a room as big as you can get so you can put a big line array in. Many speakers make a choir. Not a soloist.

A case where bigger is better IMO. Any room with treatment and appropriate equipment can work. It’s not a case of blah blah mines the biggest and best it’s what you have to work with. Much is written, videos to watch, help is readily available the end result will be satisfying.

Cheers

Largest dimension of the room can determine the accurate reproduction of the lowest frequency of your audio system. At the sea-level where speed of sound is 1,130 ft/sec, longest dimension of the room should be about 56.5/2 = 28 ft to capture one half of the 20 Hz audio signal. This calculation is based on formula v = fxw where v = velocity of sound, f = frequency, and w = wavelength. 18 ft long room can reproduce 30 Hz and 14 ft one can reproduce 40 Hz accurately.  Your speaker specifications (3dB cutoff) can be used for this calculation. This is not a requirement for subwoofers as they reproduce lower frequencies by bouncing the sound off walls many times. Above theory applies only if you want accurate reproduction of the sound.

Show-boxed shaped rooms are subjected to many room modes where you will hear certain frequencies amplified at certain locations and dead spots on other locations. A trapezoidal shaped room can minimize most of these room modes. If you have room where roof/ceiling is at an angle, then it will most likely be a trapezoidal shape or one closer to it. I understand this may not be an option for some, but at least in theory those room shapes are better than shoe-boxed shape ones. 

This is just a start. Next you have room treatment which is a very big topic covered very well on this site. Do a search.

@pwerahera 

Thank you for the really Great reply and gives something to think about related to lower frequency waves in relation to room size.

I've done dirac sound analysis of the room and find that all frequencies seem to be coming through quite well and then when enhanced with DSP for home theater it makes a huge difference, really smooths out the curve.

Thanks

The bigger is the room, the better, just as simple as that. 

The Rooms can also be evaluated on the Amount of Apertures and Aperture Dimensions.

Doors and Windows on External Walls and Internal Walls will have a strong influence on the balance of End Sound.

A Hollow Door used on the Room Entrance will most likely create a Reflected Colouration to the Sound being Produced.

It has been known for a inner panel to be produced and attached to the Internal Face of the door, where a Cavity of approx' 20mm is filled with a highly compressed fibre insulation or Koln Dried Sand. When a door is given this type of treatment there are usually additional seals used to prevent air movement between door and Door Fame and Door and Threshold.

Depending on age of Widows Air Movement might need to be controlled with a Clear Tape typically used for Winter Periods as an Air Seal on Leaky Windows.

Controlling reflections of the Glass is more complicated, but a Heavily Lined Curtain is the cheap option with limited effect. Padding the Curtain with a Fibre will help furthering the curtains function for controlling reflective sound.

https://perfectacoustic.co.uk/product-category/acoustic-curtains/

The Room is the Room, the Room will be much better as a Space to manage Sound being produced, when measures are adopted, to make sure the End Sound created by the Audio System is only heard once by the listener.

When the End Sound produced within a particular space is coming from Speakers that are adequately coupled to the space, the notion of being in a particular sized room of a particular ratio will quickly move on.

The Bliss being experienced, the sense that Sound is not adulterated and not coloured is to Supersede all other notions.   

@emergingsoul 

The larger room on your list can still be filled with modest hardware- it is not so large as to need enormous amps and speakers.  My current room is a little larger- 17 x 27 with 8-ft ceiling and I can be happy with a tube amp and KEF LS50s.  

The larger room will give you more flexibility in choosing speakers and making sure your speakers and listening spot have plenty of room to breathe.  Neither like to be close to wall boundaries!