This Spell is Problematic
Visibility is an important aspect of warfare. Many fundamental aspects of battle have emerged around this concept: from camouflage, to the high-ground, to cover, to trench warfare. Thus, any time you fundamentally change the ability of a character to restrict or enhance visibility, it brings great potential to seriously shift the tide of battle. I see this proposed spell as problematic for several reasons.
Ending the spell
Darkness is already prone to abuses, especially since a two level dip in the Warlock class can give a character access to an invocation (Devil's Sight, PHB p. 110) that can see through the spell at a range of up to 120 feet. As Daniel Zastoupil also pointed out, many monsters also have abilities (such as tremorsense or blindsight) which could allow them to see through either Darkness spell. So it is not unreasonable to imagine that the Darkness spell could be cast on creatures who cannot see through it while they are fighting creatures that can.
One major thing that prevents these abuses is that there are several ways to end or circumvent the Darkness spell. You can damage the caster (ending Concentration), simply run out of its radius (if you are the intended target), or cast Daylight. But Greater Darkness removes (or complicates) all of those options.
By removing concentration, you guarantee that if the spell is cast on yourself (or an object that you carry), there is virtually nothing that a non-magical creature can do to can be done to stop the ensuing carnage. And by increasing the radius to 60 feet, you prevent many creatures (like Goblins or Halflings) from escaping its radius in a single round. Greater Darkness could still be dispelled, but that's pretty much your only option.
Naturally, Greater Darkness should be more powerful than Darkness: any increase in spell slot level indicates at least a two level difference in character class, and 3rd level spells tend to be a particularly noticeable step up in power (hello Fireball). But it's worth noting that this increase not only improves the power of the spell, but seriously reduces the fun of working around it. Having fewer ways to end the spell means less creativity, and fewer opportunities for characters of every class to contribute to a solution to a problem.
Comparing Greater Darkness to Daylight
It's worth noting that every objection I've made about Greater Darkness applies to Daylight as well. But there is a major difference between the two spells. A caster of Daylight must be included in the spell's radius, and affected by it. A caster of Greater Darkness may (quickly) avoid one or both of these requirements.
Daylight illuminates an area in a 120 foot radius (60 feet of bright light, and 60 feet of dim light), but its range is only 60 feet. So a caster who casts daylight is almost certain to find themselves within its area of effect for at least a round or two (this can be circumvented by using a mount, but usually will be the case). Greater Darkness, by contrast, would allow a caster to encase enemies in darkness, and then step into the light by using just five feet of movement. Both spells are 3rd level spells that influence visibility, but their ability to give and restrict visibility are very different.
Also, a minor point of confusion for me would be if Daylight and Greater Darkness were both cast on a space, which would win? Both are 3rd level, and both say they cancel 3rd level spells of each others' type. It's a bit of a sticky wicket.
There are other options
There are a number of options for creating a heavily obscured area that will not be dispelled by Daylight. Amongst them are the 3rd level spells Stinking Cloud and Sleet Storm (which I just now realized heavily obscures its area of effect). Neither of these spells are prone to the abuses that Darkness can be (they aren't explicitly overcome by Devil's Sight, for example). Crucially, all the spells I have found that heavily obscure an area (at any level) require concentration. From where I'm sitting, this new spell may unbalance certain builds in the game. And even if those builds are omitted, it creates a spell with very few workarounds: that seems to me it's more likely to reduce the fun had playing the game than increase it, whether ones enemies or allies are casting the spell.