It's atmosphere would be a bit thicker, nobody knows quite how much thicker as we don't know how much dry ice there is. Thick enough so that there can be liquid water on the surface surely.
MAY BE ENOUGH CO2 TO SURVIVE WITH AN AQUALUNG TYPE ARRANGEMENT
Possibly, the Mars society think anyway, thick enough so a human can go out of doors with just an air breather, like an aqualung, rather than a full body spacesuit, and trees could grow.
ICE CAPS AND THE MISSING WATER
It would still have ice caps unless you heated it up so much it was far hotter than the Earth which is a big ask (after all Earth has ice caps). So there wouldn't be much free water if any, I think. It's ice caps are already rather small for such a large planet.
Also, the equatorial regions of Mars are thought to be probably for the most part, dry to depths of google.co.uk 100 meters or more. So probably not going to roll back to an ancient Mars with oceans and lakes.
It currently has a global equivalent layer of ice of around 30 meters. Originally had several hundred to a thousand. See Page on utinam.cnrs.fr
Nobody is quite sure what happened to all that water. Perhaps some or most escaped into space. Or maybe it sank deep underground into a deep hydrosphere kilometers below the surface. At any rate it is gone now and seems to be inaccessible for use.
Mars now has a
ICE DEPOSITS AND TEMPORARY LAKES
There are ice deposits thought to be some even in the equatorial regions but they'd just create a temporary lake and flood, as has happened often in the past, which might even last for a fair while, so you might get some lakes as happened with Gale crater. I don't think seas though.
TRYING TO MAKE OXYGEN
The atmosphere would be almost entirely CO2.
If you try to use plants to get oxygen in the atmosphere - that's probably going to take around 100,000 years.
The problem is - that you have to not just convert CO2 into organics + oxygen - but then you have to trap the organics - if they just decompose and go back into the atmosphere you've achieved nothing. So you have to keep on doing that until you've covered the entire surface with a thickness of several meters of peat or whatever it is. Then bear in mind that Mars has half the light levels of Earth. And it has about a third of its gravity so you need to create three times as much oxygen per square meter to get the same partial pressure. So Chris McKay anyway calculated it would take around 100,000 years to complete that process using ordinary photosynthesis and typical rates at which organics form on Earth by photosynthesis.
The initial heating up takes about 1,000 years in the Mars society plans. So you end up with an unbreathable atmosphere with plants, but no animals or birds or humans, after 1000 years.
UNPREDICTABILITY OF LIFE
But that's only if everything goes well. And ignoring the effect of life. Introduce life to the planet, or if there is life there already, and its very unpredictable. Because the life may not do what you want or expect it to do. May be that other species take over from the ones you want, and they may produce chemicals and gases in the atmosphere different from what you want.
EASIER FIRST - STANFORD TORUS
I think we need to try something rather easier first. E.g. try building a Stanford Torus - free floating space habitat with several square kilometers of land area. There is enough material in Deimos for instance to create Stanford Toruses with the land area of Colorado or Oregon.
If we can't make a Stanford Torus we are obviously nowhere near the technology needed to terraform an entire planet with its thousands of global greenhouse factories and thousands of square kilometers of orbiting mirrors etc etc.
But more important - if we can't keep a Stanford Torus habitat habitable, when we can control the temperature, humidity, air pressure etc, just control everything exactly as we like, and even do a reset and start again when it goes wrong - if we can't do that - then we are obviously not even remotely capable of terraforming.
AS A 58 YEAR OLD SPACE CAPABLE CIVILIZATION - DO WE NOT NEED A LITTLE MORE EXPERIENCE BEFORE WE START ON A MULTI-MILLENNIUM PROJECT?
And even if we knew how to do it - surely we have to have a little more than our present 58 so years of spaceflight before we have enough experience to do a project that has to be sustained for several thousand years to succeed?
Or we don't terraform at all.
After all terraforming a planet means you've decided you know what your descendants will need 100,000 years from now. How often do people embark on grand projects only to find when they are completed that nobody wants to use them?
Again I think it is just a little early to say that we know what we need 100,000 years from now and how to achieve it. Maybe after we have been a technological species for a few more centuries or a millennia or two we'll know better.
LIKE A BABY WITH A 100,000 YEAR GESTATION PERIOD
And it's a responsibility also. Like having a baby. But a baby that has a 100,000 year gestation period. And again I don't think myself that humans as a technological species are quite at the stage where we can take on overseeing the birth and first baby steps of a baby that needs to be monitored closely for 100,000 years.
But great and fun idea to think about and it may lead to new thoughts and approaches maybe in unexpected ways :).