Depends on the weapon category of the two-handed weapon.
A two-sided weapon only gets the same STR modifier boni as using two SH weapons, 100% STR mod on MH plus 50% STR mod on the OH weapon side, i.e. the size category does not have the same effect as with a typical large weapon, 150% STR mod..
So, if you are comparing a two-bladed sword (for instance) vs. two kukris, both do slashing damage, the same STR boni apply, but only the kukris can be finessed. The enhancement has no different effect unless it is different for each of the two SH weapons being used.
So finessable vs. non-finessable is one factor. Another could be the difference in other item properties from MH to OH, including OnHit, elemental damage type, etc. Yet another difference is in magical buffing. To imbue the two-bladed sword with GMW (again, for instance), a single cast will enhance both hands, while two casts are needed to accomplish the same effect on both SH weapons. The shield option, naturally, is only open for the two SH weapons.
Finally, though it seldom comes up, is that, each of the two SH weapons could be of different damage types. Related to a choice like this is the WM's WoC selection and fighter's WS which would require additional feats to achieve the same potential on both hands while the two-sided would only require one.
Two-sided weapons are harder to disarm than two medium, small or tiny ones.
Crit range and multiplier (in regards to the chosen weapon type) can be a factor depending on the AC being confronted. To some extent, damage type can matter (like vs. some undead).
The determination of whether a particular weapon type is "large" (and benefit from the 150% two-hand bonus) is related to race. So, a longsword wielded by a human gets only the MH damage (100% STR mod), while a gnome would be getting the two-hand bonus using the same weapon.
Character level has no effect on the two-hand bonus other than being able to pump up STR to higher levels, assuming it is a STR-focused build.
There is a rather obscure difference related to rolling multiple dice for base damage like with scythe and greatsword. The realized damage (what is actually experienced in-game), or the damage "probability", gets clustered around the average damage, with the very high and very low damages seldom experienced. With two SH weapons, every base damage possibility is equally possible (i.e. linear). This nuance become even more apparent and noticeable with critical hits.
That's about all I can think of atm. There are probably others, though.
It's typically a matter of aesthetics. Some players feel the appearance of fighting with a two-sided weapon "looks cool" so forgo any of the disadvantages..