Well...that's a pretty big difference in birds.
I'd say it comes down to what sort of companion bird you're looking for and what 'downsides' from each species you're willing to deal with (keeping in mind each bird is an individual---you may end up with a bird who because of either genetics or the way it was raised doesn't have the typical characteristics.
I own a Timneh as well, and I have found them to be slightly more outgoing than the Congo greys, she isn't afraid to talk in front of strangers or take food from them, but isn't so great about wanting to be touched by them (head scritches are an exception).
Hahns:
-if you want a more gregarious, acrobatic, hands on sort of bird who won't mind close contact
-if you want something more outgoing with more energy
-if you're a sort of active on the go person as mini-macaws don't sit still
-if you are a bit more brash in your own personality, as the hahns are a little more in-your-face
-if you want a fairly resilient bird who is less apt to be shy or afraid
CONS:
-nippy, they tend to be in my opinion much more excitable and thus will pinch you
-louder
-constant activity (for me, it'd be a minus, but for you it might not be)
Greys:
-if you are a more shy/sensitive soul, you might like the grey (they seem to be less confrontational and more empathetic) more than a macaw or amazon that tend to bolder and may not be a good match for someone who doesn't like being a bit more assertive
-if you want a calmer, less hands-on bird (don't get me wrong---greys *NEED* a lot of attention, but they're less likely to want it in the velcro-bird sort of way of being plastered on your chest or crawling on you)
-if you want a sweet, shy and yet goofy bird
-if you want an empathetic bird (i find they really watch and tune in to you and your state of being)
-if you want a quieter (comparatively) bird, they chat and whistle a lot on and off, but in terms of tone, pitch and volume they would be more likely to be quiet than the new world birds
-if you enjoy intellectual yet extremely intuitive relationships with people (greys are thinkers, and often referred to as little old men in grey suits) they are very quiet and refined and may make a good match for someone who likes to sit quiet and watch tv or read a book at night, and you may develop an almost telepathic communication between the two of you
CONS:
-if you want a bird who will be comfortable with tons of people coming over and who goes to check out everyone--this probably isn't your bird, even my timneh is unusually outgoing and she's not about to wander over to say hi anytime soon
-if you want a bird who won't be easily startled or upset (greys are notoriously sensitive and prone to feather-plucking issues)
-if you have dust allergy issues (they're a powder down bird)
-if you want a more high-energy, goofy acrobatic wrestle-and-play-puppy-with-feathers, not your bird
-if you want a cuddly velcro bird
-if you don't have the time/patience to really win them over and dedicate yourself to an almost zen state of mind and completely rethink your bird-human relationship and instead are looking for more of an easy going relationship greys *not* your bird (they do not give their hearts, trust and souls to you easily, and are quick to take it back)
-if you see yourself getting more birds/pets in the future, greys are known for being jealous and not sharing their people well at all
So...ultimately, the choice is up to you.
I love my grey, even though she frustrates me some days and I look at all the macaws and amazons and goofy little senegals etc wondering if I've made the right choice. Would I like to know what it'd be like to have a bird who would wrestle and bounce and play and not make me constantly second-guess myself and if I was doing things right ?

yup.
But it's so much more rewarding when she chooses to fly over to me and want a scritch, it makes me feel so awesome, and I enjoy the quiet respectful understanding we have and how much she is in tune with me and how much she teaches me just by reflecting myself back to me.
