Believe it or not the answer is yes. Most people don't notice because the difference is not that great, but there is a difference.
On Chanuka we read the parsha of the נשיאים, every day the נשיא for that day. Each נשיא is 6 pesukim and we have 3 aliyas. The miniumum number of pesukim for an aliya is 3. therefore we are 3 pesukim short. From where do we get the extra 3 pesukim? This is a machlokes the Mechaber and the Rama. The Mechaber writes that we simply read over that day. In other words, tomorrow morning Kohen will read the first 3 pesukim of the 5th נשיא, Levi will read the next 3, and the third aliya simply repeats all 6 pesukim of the 5th נשיא. The Rama on the other hand says, that for the third aliya you simply read the next day. In other words, tomorrow morning Kohen will read the first 3 pesukim of the 5th נשיא, Levi will read the next 3, and the third aliya reads the 6th נשיא. In חו"ל the minhag is like the Rama and in EY the minhag is like the mechaber.
The Gra points out that this is לשיטתם by chol hamoed succos. On chol hamoed succos the problem is greater, each day is only 3 pesukim and there are 4 aliyos. According to the Mechaber in חו"ל kohen and levi read the 2 days of sefeka d'yoma and then the next 2 aliyas simply repeat them. The Rama writes that שלישי reads the next day, meaning if today is the first day of Chol Hamoed, the first 2 aliyas read days 2 and 3 and the third aliya reads day 4, even though it is clearly not day 4 even with the sefeka d'yoma, and רביעי goes back on the first 2 days. In EY the machaber writes that we simply repeat the same thing 4 times. Here also the minhag in EY is like the mechaber.
The machlokes would seem to be does the next day have any connection to today and does it make sense to read it.
Interestingly enough the Ashkenazim in EY are noheg like the Mechaber both on Succos and on Chanuka.