My favorite explanation what the difference between D&D editions is in a question: “How many arrows does it take to kill a level 1 wizard?”. The reason why this question is so revealing is that the answer to it is so different in the different editions. In first edition AD&D a single arrow can kill a level 1 wizard, in 4E you need at least 4 arrows, and in D&D Next the number is in between. Thus if you have an encounter which is an ambush and starts with level 1 archers attacking a level 1 group, the encounter would be extremely deadly in 1st edition, and much less so in 4th edition. You can’t just change the stat blocks and pretend this will give the same result regardless what edition is being run.
Of course that is just an example, and the fundamental differences don’t stop there. But anybody who ran some of the D&D Next playtest material has seen that D&D Next tends towards a series of small encounters, while 4th edition tends towards a much smaller number of encounters, which are more tactical and more epic. It would be hard to design an adventure in which this wouldn’t matter one way or another.
The differences between the editions aren’t limited to the combat part. D&D Next, as the previous editions, has many of the “classic” wizard spells which are extremely powerful in non-combat situations. Anybody who ever ran a D&D campaign of earlier editions will be aware of the problems with spells like invisibility or flying: They make the wizard of the group far more powerful in exploration than other classes. Why play a rogue with an x% chance of hiding in shadows if you can play a wizard and just be totally invisible? 4th edition sensibly removed many of the overly powerful non-combat spell (which is why 98% of the people who complain vocally about 4th edition are those who played a wizard or similar overpowered spellcaster in earlier editions. A better balanced game is not in the interest of those who abused the previous imbalance.).
Assuming that “Storm over Baldur’s Gate” is a city adventure, there are a lot of possible problems that can arise by switching from one edition to another. For example the ability of speaking with the dead, another D&D classic, is wreaking havoc with murder mystery plot lines, usually requiring some sort of strange Deus Ex Machina device preventing it. Detect Evil or Detect Lie spells are similarly disruptive for an investigative adventure. (Note to Stubborn: Have you thought of that?)
In short: Players have a tendency to look for options on their character sheet. Having two groups with different editions of character sheets in front of them facing the same adventure might have some unintended results. There might be more changes to an adventure necessary than just changing the stat blocks.