While Michael VII undoubtedly behaved very poorly and his actions did have some negative consequences, to describe the only Roman Emperor post-1204 to successfully outmanoeuvre the West and maintain the Empire as a significant power as "one of the very worst" is completely unfair. Any Nicaean Emperor to recapture Constantinople would have been faced with the same challenges from the West, and most would have found themselves losing all of Europe at a minimum. The Laskarids certainly would have struggled to pull off the religious agility that preserved Roman power for several decades. Michael did indeed end up failing, facing almost insurmountable odds, but it would have taken a very lucky and very competent Emperor to do substantially better while holding Constantinople.
To answer the OP, had the Laskarids remained at the helm of the Empire they would have had a stronger position in Anatolia and likely more internal cohesion... so long as they still get rid of Mouzalon. Many on this site talk about the Roman aristocracy as if it were some entirely parasitic entity that would happily allow the Empire to fall for their own financial benefit or some other cynical goal, but the reality is that any administration that fails to manage the elite members of their society is going to be faced with rebellion and conflict. Mouzalon was extremely unpopular; he had to go. Otherwise he's an albatross. Presuming they can ditch him somehow, and for the sake of the argument assuming they can nab Constantinople in similar circumstances, then... not a lot will be immediately different. The West will be coming for them, Charles of Anjou or not. Constantinople is too important a prize to give up without a fight. I seriously doubt the Laskarids will be able to prevent this. Actually taking Constantinople is no mean feat, but the Roman territory in Europe is extremely vulnerable.
In Anatolia the Romans were overrun for more reasons than 'fighting in Europe'. Laskarid popularity will help, but the Turkish tide will be difficult to resist. Characters such as Philanthropenos had some success in resisting, but it will take quite a vital Empire to successfully absorb the Turkish tide. They certainly won't succeed if Constantinople is lost, nor will they have a better shot if the army is wrecked fighting Latins. It was not impossible OTL for them to succeed, but I don't think the Laskarids were substantially better placed than the Palailogoi to do so. The reality for the 13th century Romans was that their challenges were much more external than internal.