I'd go for the room any time.   Largely what you are hearing is "reverb" rather than "echo" - but - that's a moot point.   Reverb is commonly added to studio recorded vocals, for instance - a mixed-in "delay" of 10-to-30 mSec, possibly repetitively added in at lower and lower amplitudes.   Precisely "how" this echo/reverb is perceived is quite a complex process in the brain - both by the player and the listeners.

Reverb gives an added "richness" and "interest" to the sound.   In fact, if playing as a solo with no other instruments or backing, added reverb (natural from the room, or electronically) can bring what could otherwise be a "relatively uninteresting" sound, to life.  It is this lack of reverb you experience when playing in the clothing cupboard.

For solid-body electric instruments such as the electric violin or guitar which lack the natural resonances from the sound-box it is virtually recognized as standard procedure to electronically add various effects, reverb being one of the most important.  Without it, I describe the EV sound as "sterile", lacking interest.

"Echo" as such, to my mind anyway - is much the same as reverb, it's just that it would involve a much longer delay and would arrive back at the originators ears as a quite distinct, and separate sound - like shouting "Helloooo" in a quarry or whatever and some noticeable time later hearing it coming back at you....   whereas with a much much shorter delay in "reverb" the reflected sound is being actively mixed with and added to, the original....

I suppose there would be a sort of limit on just how much reverb you would be willing to live with before the sound just became too "boomy" for your liking, but that would more likely occur in a large (and empty of audience) hall.

Both sound production and a listener's perception of it can be quite a complex thing to describe - it's like "you have to be there" LOL

Just my thoughts....  but I'd stick with the room "echo" - besides - you'd have a very limited audience playing in the cupboard !!!!

My brother recommended playing in the closet to help absorb some of the sound.

Are you sure he doesn't have a hidden agenda here ?   I'm just kidding with you ! 

Yup - I go back to my original response to the post - if I'm in "play" mode - yes - for me, I stand by what I said - I like the room echo - our lounge is good - hardwood floors, not much soft furnishings, it's good to both my ear and the recording mic.

Bathroom - sure tried it - in our one it's a tad too "boomy" for me but has it does have its own very distinctive sound...  I can't quantify it - maybe if the bathroom were larger the "returning echoes" would be further apart ?   Dunno - I mean we're only talking milliseconds here.... but of course it's also the "decay time" as well - I suspect that's maybe what irritates me.  Really not sure yet.... some things I play there sound good under the ear - some ( usually faster pieces ) just don't....

BUT - as @Demoiselle says - when it comes to "practice" as distinct from "playing live" - sure - the "dry" sound works well for me and I find this really "telling" and shows up a lot of my inaccuracies - and I achieve that largely by going to the EV.   My description of the EV sound is "sterile" - with no body resonances to speak of, and virtually no inter-string resonances ( OK, very little - there are some I can hear depending on what I'm doing) it's getting close in some ways to the "dry" sound from an acoustic ( in fact, it is IMO an even MORE telling test with no body resonances. than you would have from a really-dry acoustic... )

I think we need to experience both types of acoustic environment, just to get a real feel for sound production form the instrument....

It is also quite telling to record, with a reasonable studio mic, your sound, and play back on reasonable speakers (not your tinny little inbuilt laptop speakers) or quality headphones...   it sounds quite different from what it does "under your ear whilst playing"....  especially in a wet acoustic - your ear is SO much closer to the sound output of the fiddle you're getting "more of that" to your ear compared to the level of room-reverb coming at you.... a well placed mic and a listen-back can tell a lot about how it might sound to a listener...

It's all about your ear - and your listeners' ears - often quite different things...

I can see some experiments coming up when I can find sometime...  Also quite interested in playing out-doors ( I have done in the past ) - but to take some proper measurements - but gonna have to wait till spring-time for that..

As it happens - here's my 4/4 fiddle restrung as a viola, playing outside, it sounds QUITE different - BOTH under the ear and to the mic - from when played and recorded indoors....  this was about a year ago... on holiday in the hills above Braemar - until I was interrupted by a hill-walker !